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5,713,212 | https://en.wikipedia.org/wiki/Humane%20education | Humane education is broadly defined as education that nurtures compassion and respect for living beings In addition to focusing on the humane treatment of non-human animals, humane education also increasingly contains content related to the environment, the compassionate treatment of other people, and the interconnectedness of issues pertaining to people and the planet. Humane education encourages cognitive, affective, and behavioral growth through personal development of critical thinking, problem solving, perspective-taking, and empathy as it relates to people, animals, the planet, and the intersections among them. Education taught through the lens of humane pedagogy supports more than knowledge acquisition, it allows learners to process personal values and choose prosocial behaviors aligned with those values.
History
Humane education as a discrete field of education was created in the late 1800s by individuals like George Angell as an attempt to address social injustices and prevent cruelty to animals before it started along with the formation of SPCAs, such as the Massachusetts SCPA and the ASPCA. The formation of humane education and animal protection/welfare organizations was associated with the expansion of women’s suffrage and the temperance movement, and many of those involved in creation and early advocacy of humane education also worked in those other areas of social change as well. These early activists successfully advocated for the passage of laws supporting or even requiring the teaching of humane education in schools, and many teachers did teach it. The animal welfare organizations also visited schools and other youth centers to teach “push-in” programs that supplemented—and possibly augmented—the children’s other education.
In addition to school-based programs and activities, humane education was also initially conducted through Bands of Mercy; although these have been disbanded, humane education continues to be conducted in community-based settings. These include animal shelters, humane education centers and parks as well as, e.g., Boys and Girls Clubs, YWCAs and YMCAs, cultural and religious centers, etc.
Currently, humane education is often conducted by animal welfare organizations and organizations that include humane education among their primary focuses.
General Goals, Content, and Pedagogical Strategies
Humane education seeks to nurture the development of compassion and concern that people—especially children and adolescents—have towards one group (e.g., humans) be extended to other groups (e.g., animals). One of the beliefs that helped establish humane education as a field has been that helping children learn to treat animals with kindness will encourage them to grow up to be adults who are kind to all animals, human and non-human. This “cross-fertilization” of kindness is also used, e.g., to try to have the care that children have for their own pets be extended to animals in their community, animals in circuses and zoos, animals in agriculture and on factory farms, or to show how reducing pollution in one’s neighborhood can help ecosystems far away.
Typical Current Content
In addition to the humane treatment of domestic animals, humane education now often examines broader issues including human relationships and animal exploitation. Common topics currently covered include responsible pet care (e.g., spaying/neutering and responsible adoption); animal agriculture; factory farming; captive wild animals; understanding animal emotions, sentience, and communication; blood sports; bite prevention; ecological stewardship; the interconnectedness of life; pollution; reduction/reuse/recycling of materials; bullying; non-violent conflict resolution; critical thinking, child labor; and the effects of every-day activities on other people, animals, and the environment.
Pedagogical Strategies
Since the beginning, humane education has focused on a constructivist approach to teaching and includes methods such as service-learning and experiential learning. Organizations that conduct humane education programs, therefore, often create community- or home-based activities in which students can learn humane education content and behaviors through experience and reflection.
Humane education programs may be conducted in a variety of ways in schools. Programs may be supplemental or add-on programs such as when a humane educator or the teacher of record will devote a class period to humane education content; in these cases, the lesson is often devoted wholly to teach humane education content (e.g., responsible pet or environmental care, spaying/neutering, respect for others). Programs may also be infused into the curriculum or add-ins. These infused programs allow for the most effective form of Humane Pedagogy (a teaching approach inspired by critical pedagogy, which attempts to help students activate cognitive, affective, and psychomotor domains of learning and determine personal values with an ecocentric lens.) The strongest humane pedagogy is part of both the written and unwritten curriculum.
Humane education may also be integrated into traditional lessons. Since most children and adolescents find animals and nature to be engaging topics, humane education can be an effective vehicle to also teach other content, such as literature, history, civics, or science.
Effectiveness
Although teachers who use humane education often report anecdotal evidence that it works, and although there is a welter of qualitative research that also suggests it is effective, there are few objective, well-controlled studies that compare humane education programs against good control groups. Nonetheless, those who have studied it carefully tend to find that it is effective---probably at least as effective as other, comparable non-humane education programs.
Animal-Assisted Education
Animal-assisted education is education that is employs direct interaction/perception of animals to enhance learning. One such program used shelter dogs in a school-based violence prevention and character education program. According to the researcher, "[f]indings indicate that receiving the program significantly alters students’ normative beliefs about aggression, levels of empathy, and displays of violent and aggressive behaviors".
School-based Programs
Probably the largest study of humane education ever conducted included a "large evaluation conducted over 3 separate years in 25 public elementary schools in 5 cities across eastern China". The author randomly assigned about half of the schools to participate in Caring-for-Life, a humane education program, and randomly assigned the other half to the control group. In all, the effect of the program was tested on over 2,000 first and second grade students. The author reports that "[s]tudents who participated in the program displayed significantly greater gains in prosociality than similar students who didn’t. Students who participated in an expanded version of the program appeared to realize even greater gains".
Another large-scale, randomized control trial found that a 12-lesson humane education program significantly improved lower elementary students' attitudes and behaviors about the environment. The humane education program was taught by the students' teachers during one period of the normal school day over one academic year. By the end of the year, the children who participated in the program reported caring more about a range of environmental issues and that they engaged in more behaviors to address these issues (than did peers who did not participate in the humane education program). The humane education program that was studied was designed to address the United Nationals Educational, Scientific, and Cultural Organisation's (UNESCO's) Four Pillars of Education through both humane education strategies and content.
Another experimental-vs-control study compared the effect of the HEART humane education program on elementary students in several schools in two cities in the United States. Students self-reported their attitudes about the treatment of animals and the environment, and teachers rated each student's prosocial and disruptive behaviors. The authors found that "the development of prosocial behaviors and self-reported attitudes significantly interacted with group assignment: Students who participated in the humane education program showed stronger growth in both of these outcomes compared with students in the control group". However, they did not find changes in disruptive behaviors to differ between the groups. Overall, the authors state that "[t]he results support the effectiveness of a humane education program to teach a relatively large and diverse group of upper elementary students to learn about animal welfare issues and to improve their prosocial behaviors. Effects appeared strongest on attitudes; behavioral effects were found to be largely limited to behaviors directly addressed by the humane education program."
Duration of Effects
The effects of a humane education program seem to last for at least a year. Piek and colleagues found that young children randomly assigned to participate in the Animal Fun program, which "was designed to enhance motor and social development in young children" showed significant improvements in teacher-rated prosocial behaviour and total difficulties compared to children randomly assigned to the control group. The effect of the program was found to still be strong not only 6 months but also 12 and 18 months later. As the authors states, "The Animal Fun program appears to be effective in improving social and behavioural outcomes".
List of Humane Education Organizations
Bands of Mercy
Factory Farming Awareness Coalition
InterNICHE
See also
Animal-assisted interventions
Animal cruelty
Anti-vivisection movement
Animal welfare
Environmental education
Environmental protection
Ecopedagogy
Human rights
Social justice
Sustainability
Vegetarianism, Veganism
References
Further reading
Unti, B. & DeRosa, B. (2003). Humane education: Past, present, and future. In D. J. Salem & A. N. Rowam (Eds.), The State of the Animals II: 2003 (pp. 27 – 50). Washington, D.C.: Humane Society Press
Alternative education
Animal welfare
Anti-vivisection movement | Humane education | [
"Chemistry"
] | 1,910 | [
"Animal testing",
"Anti-vivisection movement",
"Vivisection"
] |
5,713,217 | https://en.wikipedia.org/wiki/Transdermal%20spray | A metered-dose transdermal spray (MDTS) delivers a drug to the surface of the skin and is absorbed into the circulation on a sustained basis. It works in a similar manner to a transdermal patch or topical gel. The drug is delivered by a device placed gently against the skin and triggered, causing it to release a light spray containing a proprietary formulation of the drug that quickly dries on the skin to form an invisible drug depot. As it would be from a patch, the drug is then absorbed steadily for a predetermined amount of time.
References
Drug delivery devices
Dosage forms | Transdermal spray | [
"Chemistry"
] | 125 | [
"Pharmacology",
"Drug delivery devices"
] |
5,713,883 | https://en.wikipedia.org/wiki/Instruction%20step | An instruction step is a method of executing a computer program one step at a time to determine how it is functioning. This might be to determine if the correct program flow is being followed in the program during the execution or to see if variables are set to their correct values after a single step has completed.
Hardware instruction step
On earlier computers, a knob on the computer console may have enabled step-by-step execution mode to be selected and execution would then proceed by pressing a "single step" or "single cycle" button. Program status word / Memory or general purpose register read-out could then be accomplished by observing and noting the console lights.
Software instruction step
On later platforms with multiple users, this method was impractical and so single step execution had to be performed using software techniques.
Software techniques
Instrumentation - requiring code to be added during compile or assembly to achieve statement stepping. Code can be added manually to achieve similar results in interpretive languages such as JavaScript.
instruction set simulation - requiring no code modifications for instruction or statement stepping
In some software products which facilitate debugging of High level languages, it is possible to execute an entire HLL statement at a time. This frequently involves many machine instructions and execution pauses after the last instruction in the sequence, ready for the next 'instruction' step. This requires integration with the compilation output to determine the scope of each statement.
Full Instruction set simulators however could provide instruction stepping with or without any source, since they operate at machine code level, optionally providing full trace and debugging information to whatever higher level was available through such integration. In addition they may also optionally allow stepping through each assembly (machine) instruction generated by a HLL statement.
Programs composed of multiple 'modules' compiled from a mixture of compiled languages, and even instructions created "on-the-fly" in dynamically allocated memory, could be accommodated using this technique.
Examples of programs providing 'Software' instruction step
SIMMON an IBM internal test system which provided instruction stepping
References
See also
Instrumentation (computer programming)
Instruction set simulator
Program status word
Instruction cycle
Debugging | Instruction step | [
"Technology"
] | 424 | [
"Computing stubs",
"Computer science",
"Computer science stubs"
] |
5,715,611 | https://en.wikipedia.org/wiki/Las%20Cumbres%20Observatory | Las Cumbres Observatory (LCO) is a network of astronomical observatories run by a non-profit private operating foundation directed by the technologist Wayne Rosing. Its offices are in Goleta, California. The telescopes are located at both northern and southern hemisphere sites distributed in longitude around the Earth. For some astronomical objects, the longitudinal spacing of telescopes allows continuous observations over 24 hours or longer. The operating network currently consists of two 2 meter telescopes, nine 1 meter telescopes, and seven 40 cm telescopes, placed at six astronomical observatories. The network operates as a single, integrated, observing facility, using a software scheduler that continuously optimizes the planned observing schedule of each individual telescope.
History
Rosing incorporated Las Cumbres Observatory in 1993 with the goal of aiding universities, observatories, and individuals in the acquisition and improvement of telescopes, optics, and instrumentation. He also set the objective for the organization to build and implement a global telescope system. In 2005, Rosing established the global telescope version of Las Cumbres Observatory.
LCO initially acquired the two Faulkes 2 meter telescopes. Faulkes Telescope North (FTN) located at Haleakala Observatory, on Maui, Hawaii, and Faulkes Telescope South (FTS) at Siding Spring Observatory (SSO), in eastern Australia. LCO also purchased the company that built the Faulkes telescopes, Telescope Technologies Limited of Liverpool, with the intent of installing additional 2-meter telescopes at different sites to form a robotically operated network. Over the next few years, Rosing and the LCO staff came to understand that a network composed of many smaller telescopes would provide greater observing capacity. The organization designed its own 1 meter telescope with a plan to locate several of these at each chosen site. An even smaller 40 cm telescope was also developed primarily for use in education projects.
During 2012 and 2013, nine 1 meter telescopes were constructed and deployed to McDonald Observatory at Fort Davis, Texas; Cerro Tololo Interamerican Observatory (CTIO) in Chile; South African Astronomical Observatory (SAAO), near Sutherland, South Africa; and SSO in Australia. During 2015 and 2016, seven 40 cm telescopes were deployed to CTIO, Haleakala Observatory, SSO, and to Teide Observatory on Tenerife in the Canary Islands.
After completion of the construction and installation of these telescopes, LCO began its transition to operating a global observatory. In 2013, a Board of Directors was established and a President was hired to lead the organization. Full science scheduling began on 1 May 2014, with the two 2 meter and nine 1 meter telescopes operating as a single, integrated, observatory. The 40 cm telescopes were added to this system as they were commissioned.
The National Science Foundation made an award to LCO in 2016 through its Mid-Scale Innovations Program, purchasing access to the LCO network for all astronomers at U.S. institutions. The goal of this program is to prepare this community to carry out effective research following discoveries being made by current and future time domain astronomy surveys.
Telescope network
Sites
LCO operates its network at seven sites. The operating sites are all professional astronomical observatories.
In the southern hemisphere:
Cerro Tololo Interamerican Observatory (CTIO) in Chile
South African Astronomical Observatory (SAAO), near Sutherland, South Africa
Siding Spring Observatory (SSO), in eastern Australia
In the northern hemisphere:
McDonald Observatory at Fort Davis, Texas
Haleakala Observatory, on Maui, Hawaii
Teide Observatory on Tenerife in the Canary Islands
The Ngari Observatory in Ngari Prefecture, western Tibet, China was added as a node to the network.
LCO also operates an identical 1 meter telescope at its headquarters in Goleta for engineering development and a 0.8 meter telescope at Sedgwick Reserve near Santa Ynez, California.
Telescopes
The 2 meter telescopes are the two Faulkes telescopes built by Telescope Technologies Ltd. They are f/10 Ritchey-Chrétien optical configurations on alt-az mounts.
The 1 meter telescopes are f/7.95 Ritchey-Chrétien optical systems on equatorial mounts. They have a 50 arcminute-diameter fully corrected field of view.
The telescopes use the optics and tubes from Meade 16 inch RCX telescopes. The mount has been replaced by a scaled-down version of the LCO 1 meter telescope mount.
Instruments
The 2 meter telescopes are instrumented with optical imagers and low-resolution optical spectrographs (FLOYDS).
The 1 meter telescopes are instrumented with “Sinistro” optical imagers that have a 26 arcminute square field of view. During 2017, a set of high-resolution (R = 50,000), high-stability spectrographs (NRES) were deployed to four of the LCO sites to be coupled by optical fibres to the 1 meter telescopes.
The telescopes are equipped with SBIG STX-6303 optical imagers.
Operation
The global telescope network operates as a single observatory. Users request observations only for a generic class of telescope/instrument and the software scheduler determines an optimum observing schedule for each telescope. The scheduler revises the observing schedules for all telescopes as necessary and updates can be provided within 15 minutes. The rapid-response request mode bypasses the scheduler and can begin an observation within a few minutes after submission. Each telescope carries out a nightly calibration program and adjusts its pointing and focus several times per night.
The telescopes are all instrumented uniformly to facilitate the combining of data from multiple telescopes or sites. Data are returned to LCO headquarters, where they are processed to remove instrumental signature and ingested into an archive. Users have immediate access to their observations and all data are made public after 12 months.
Usage
The network is available to researchers at institutions that are members of the LCO science collaboration. Institutions that operate the sites hosting the LCO telescopes and a few institutions that have contributed resources to help build the network are members of the collaboration. The entire U.S. astronomical community gained access to the LCO network in 2016 as a result of an award from the National Science Foundation's Mid-Scale Innovation Program. The program is administered through a peer-review proposal process run by the National Optical Astronomy Observatory. Several science teams and individuals also purchase time on the LCO network.
Research
The design and operation of the LCO global telescope network provide the unique capabilities required for time domain astronomy. The LCO network offers the ability to observe objects or events continuously and the ability to obtain data rapidly upon the discovery or announcement of an event.
The LCO network has been used to study supernovae and other explosive transients; exoplanets, through observations of both transits and microlensing; asteroids; and AGN variability. In 2017 LCO played a critical part in two major discoveries: first visible counterpart of a gravitational wave event, and a new type of supernova with successive explosions.
Education
Since the beginning of LCO, education has been one of its core missions. In 2017, for the first time in LCO's history it issued an open call for education partners, Global Sky Partners—groups who could use their robotic telescopes to inspire diverse audiences with educational and outreach projects that they support. In 2019 there are 20 LCO Global Sky Partners based in the US, Europe, Sub-Saharan Africa, the Middle East, Australia, or running entirely online programs, for students, teachers, and the wider public. In 2019 the reported direct impact of the program was 13,000 individuals exclusively using the LCO 0.4-meter network, predominantly school children and teachers.
The LCO education team also maintains in-house educational programs to trigger observations and make use of data from the LCO network. These programs are designed to inspire anyone with an interest in astronomy to explore science using robotic telescopes. Recent successful programs include Asteroid Tracker, Agent Exoplanet, and Serol's Cosmic Explorers.
See also
List of astronomical observatories
Lists of telescopes
Time-domain astronomy
RoboNet
References
External links
Las Cumbres Observatory official website
Astronomical observatories in California
Astronomical observatories in Hawaii
Astronomical observatories in Texas
Buildings and structures in Maui County, Hawaii
Non-profit organizations based in California
Telescopes | Las Cumbres Observatory | [
"Astronomy"
] | 1,698 | [
"Telescopes",
"Astronomical instruments"
] |
5,715,706 | https://en.wikipedia.org/wiki/List%20of%20silicon%20producers | This is a list of silicon producers. The industry involves several very different stages of production. Production starts at silicon metal, which is the material used to gain high purity silicon. High purity silicon in different grades of purity is used for growing silicon ingots, which are sliced to wafers in a process called wafering. Compositionally pure polycrystalline silicon wafers are useful for photovoltaics. Dislocation-free and extremely flat single-crystal silicon wafers are required in the manufacture of computer chips.
Polysilicon producers
Polysilicon producers:
Elkem
JFE Steel
Nitol Solar (Russia), bankrupt since 2019
SunEdison
SolarWorld
High-purity silicon
Producers of high-purity silicon, an intermediate in the manufacture of polysilicon
Hemlock Semiconductor Corporation
Renewable Energy Corporation (REC)
SunEdison
Tokuyama Corporation
Wacker Chemie AG
Silicon wafer manufacturers
A partial list of major producers of wafers (made of high purity silicon, mono- or polycrystalline) includes:
GlobalWafers
Okmetic
Renewable Energy Corporation
Shin-Etsu Handotai
Siltronic
SUMCO
WaferPro
Pure Wafer
See also
List of photovoltaics companies
References
Silicon
Silicon | List of silicon producers | [
"Chemistry"
] | 252 | [
"Semiconductor materials"
] |
5,715,765 | https://en.wikipedia.org/wiki/Putlog%20hole | Putlog holes or putlock holes are small holes made in the walls of structures to receive the ends of poles (small round logs) or beams, called putlogs or putlocks, to support a scaffolding. Putlog holes may extend through a wall to provide staging on both sides of the wall.
A historically common type of scaffolding, putlog holes date from ancient Roman buildings. The term putlock and the newer term putlog date from the 17th century and are still used today. Putlogs may be supported on the outer ends by vertical poles (standards), cantilevered by one end being firmly embedded in the wall, or cantilevered by penetrating the wall to provide scaffolds on both sides. Putlogs may be sawn off flush with the wall if they cannot be removed, but exterior putlog holes are typically filled in as the scaffold is removed to prevent water from entering the walls. Interior putlog holes may be left open, particularly if not in a finished space.
The inconsequential size and the spacing of the holes meant that they did not affect the solidity of the walls, and in well-preserved castles, like Beaumaris, the ancient putlog holes can be seen to this day.
Gallery
See also
Viga (architecture)
References
Castle architecture
Medieval architecture
Architectural elements
Scaffolding | Putlog hole | [
"Technology",
"Engineering"
] | 281 | [
"Building engineering",
"Architectural elements",
"Components",
"Architecture"
] |
5,715,923 | https://en.wikipedia.org/wiki/List%20of%20mergers%20and%20acquisitions%20by%20IBM | IBM has undergone a large number of mergers and acquisitions during a corporate history lasting over a century; the company has also produced a number of spinoffs during that time.
The acquisition date listed is the date of the agreement between IBM and the subject of the acquisition. The value of each acquisition is listed in USD because IBM is based in the United States. If the value of an acquisition is not listed, then it is undisclosed.
Precursors 1889–1910
Herman Hollerith initially did business under his own name, as The Hollerith Electric Tabulating System, specialising in punched card data processing equipment. In 1896 he incorporated as the Tabulating Machine Company.
1889 Bundy Manufacturing Company incorporated.
1891 Computing Scale Company incorporated.
1893 Dey Patents Company (soon renamed the Dey Time Register Company) incorporated.
1894 Willard & Frick Manufacturing Company (Rochester, New York) incorporated.
1896
Detroit Automatic Scale Company incorporated.
Hollerith incorporates the Tabulating Machine Company. Will be reincorporated in 1905.
1899 Standard Time Stamp Company acquired by Bundy Manufacturing Company.
1900
International Time Recording Company incorporated, acquiring the time-recording business of the Bundy Manufacturing Company and the Willard & Frick Manufacturing Company (Rochester).
Chicago Time-Register Company acquired by International Time Recording Company.
Dayton Moneyweight Scale Company acquired by Computing Scale Company.
Detroit Automatic Scale Company acquired by Computing Scale Company.
1905 Hollerith reincorporates as The Tabulating Machine Company.
1907 Dey Time Register Company acquired by International Time Recording Company.
1908 Syracuse Time Recorder Company acquired by International Time Recording Company.
Computing-Tabulating-Recording Company, 1911
Since the 1960s or earlier, IBM has described its formation as a merger of three companies: The Tabulating Machine Company (1880s origin in Washington, DC), the International Time Recording Company (ITR; 1900, Endicott), and the Computing Scale Company of America (1901, Dayton, Ohio). However, there was no merger, it was an amalgamation, and an amalgamation of four, not three, companies. The 1911 CTR stock prospectus states that the Bundy Manufacturing Company was also included.
While ITR had acquired its time recording business in 1900 Bundy had remained a separate entity producing an adding machine and other wares.
The Tabulating Machine Company
Computing Scale Corporation
International Time Recording Company
Bundy Manufacturing Company
CTR owned the stock of the four companies; CTR neither produced nor sold any product; the four companies continued to operate, as before, under their own names.
Acquisitions during 1912–1999
1912–1929
1917
American Automatic Scale Company acquired as International Scale Company.
CTR consolidates three already-existing Canadian companies: The Canadian Tabulating Machine Co., Ltd, the International Time Recording Co. of Canada, Ltd., and the Computing Scale Co. of Canada, Ltd., in a new holding company, International Business Machines Co., Ltd.
1921
Pierce Accounting Machine Company (asset purchase).
Ticketograph Company (of Chicago).
1923
Dehomag
1924
CTR was renamed "IBM".
1930–1949
1930 Automatic Accounting Scale Company.
1932 National Counting Scale Company.
1933 The separate companies were integrated in 1933 as IBM and the holding company eliminated.
1933 Electromatic Typewriters Inc. (See: IBM Electromatic typewriter)
1941 Munitions Manufacturing Corporation.
1950–1969
1959 Pierce Wire Recorder Corporation.
1964 Science Research Associates.
1970–1989
1974 CML Satellite Corporation; renamed Satellite Business Systems (SBS).
1984 ROLM
1986 RealCom Communications Corporation.
1990–1999
1993
CGI Informatique (France), bought in 1993, ran independently until 1996, and was then progressively absorbed by IBM, country by country, this process being achieved in 1999.
1994
Transarc (Transarc Corporation bought by IBM in 1994, became part of IBM proper in 1999 as the IBM Pittsburgh Lab)
1995
Lotus Development Corporation for $3.5 billion.
Information Systems Management Canada (ISM Canada)
K3 Group Ltd.
Chrysler Systems Leasing (February 1995)
1996
Wilkerson Group
Tivoli Systems, Inc. for $743 million.
Data Sciences Ltd, prior to 1991 comprising Thorn EMI Software, Datasolve and the Corporate Management Services Division of Thorn EMI, for £95 million.
Object Technology International (OTI) is acquired by IBM
Cyclade Consultants (Netherlands)
Fairway Technologies
Professional Data Management, Inc. / LifePRO
1997
Software Artistry for $200 million.
Unison Software.
Dominion Semiconductor (Manassas, VA) is created by forming a 50/50 joint venture with Toshiba to produce 64MB and 256MB DRAM chips. Administrative offices are located in Building 131 the former IBM Federal Systems campus now primarily owned by Lockheed Martin; the new state-of-the-art fabrication facility was built from on adjacent land.
1998
CommQuest Technologies.
DataBeam Corporation, Lexington, KY
Ubique Ltd., Israel
1999
Dascom Technologies (USA), A subsidiary of Dascom Holdings.
Mylex Corporation.
Sequent Computer Systems for $810 million.
Acquisitions since 2000
Number of acquisitions per year according to table below:
In 2020 IBM acquired 5 companies
In 2019 IBM acquired 1 companies
In 2018 IBM acquired 3 companies
In 2017 IBM acquired 3 companies
In 2016 IBM acquired 12 companies
In 2015 IBM acquired 13 companies
In 2014 IBM acquired 4 companies
In 2013 IBM acquired 9 companies
In 2012 IBM acquired 9 companies
In 2011 IBM acquired 8 companies
Spin-offs
1934 – Dayton Scale Division is sold to the Hobart Manufacturing Company.
1942 – Ticketograph Division is sold to the National Postal Meter Company.
1958 – Time Equipment Division is sold to the Simplex Time Recorder Company.
1974 – Service Bureau Corporation sold to Control Data Corporation
1984 – Prodigy, formerly a joint venture with Sears, Roebuck and Company.
1985 – Satellite Business Systems sold to MCI Communications
1988 – Copier/Duplicator business, including service and support contracts, sold to Eastman Kodak.
1990 – ARDIS mobile packet network, a joint venture with Motorola. Motorola buys IBM's 50% interest in 1994. Now Motient.
1991 – Lexmark (keyboards, typewriters, and printers). IBM retained a 10% interest. Lexmark has sold its keyboard and typewriter businesses.
1991 – Kaleida, a joint Multimedia software venture with Apple Computer.
1992 – Taligent, a joint software venture with Apple Computer.
1992 – IBM's personal computer manufacturing divisions, combined and spun off to form the autonomous subsidiary IBM Personal Computer Company (later IBM Personal Systems Group).
1992 – IBM Commercial Multimedia Technologies Group, spun off to form private company Fairway Technologies.
1992 – IBM sells its remaining 50 percent stake in the Rolm Company to Siemens A.G. of Germany.
1994 – Xyratex enterprise data storage subsystems and network technology, formed in a management buy-out from IBM.
1995 – Advantis (Advanced Value-Added Networking Technology of IBM & Sears), a voice and data network company. Joint Venture with IBM holding 70%, Sears holding 30%. IBM buys Sears' 30% interest in 1997. AT&T acquires the infrastructure portion of Advantis in 1999, becoming the AT&T Global Network. IBM retained business and strategic outsourcing portions of the joint venture.
1994 – Federal Systems Division sold to Loral becoming Loral Federal Systems. The Federal Systems Division performed work for NASA. Loral was later acquired by Lockheed Martin.
1996 – Celestica, Electronic Manufacturing Services (EMS).
1998 – IBM Global Network sold to AT&T to form AT&T Business Internet.
1999 – Dominion Semiconductor (DSC) IBM sells its 50% share to JV partner Toshiba. DSC becomes a wholly owned subsidiary of Toshiba.
2001 – Information Services Extended department, developer of specialized databases and software for telephone directory assistance, is spun off to form privately held company ISx, Inc (later sold to Local Matters).
December 31, 2002 – IBM sells its HDD business to Hitachi Global Storage Technologies for approximately $2 billion. Hitachi Global Storage Technologies now provides many of the hardware storage devices formerly provided by IBM, including IBM hard drives and the Microdrive. IBM continues to develop storage systems, including tape backup, storage software and enterprise storage.
December 2004 – Acquisition of the IBM PC business by Lenovo: Lenovo acquires 90% interest in IBM Personal Systems Group, 10,000 employees and $9 billion in revenue.
April 3, 2006 – Web analytics provider Coremetrics acquires SurfAid Analytics, a standalone division of IBM Global Services. The deal was said to be in the "eight-figure" range, making it worth at least $10 million. (Note: Since then Coremetrics has in turn been acquired by IBM)
January 25, 2007 – Three-year joint venture with IBM Printing Systems division and Ricoh to form new Ricoh-owned subsidiary, InfoPrint Solutions Company, for $725 million.
September 2009 – IBM launches online business IT video advice service in association with GuruOnline.
September 2009 – IBM sells its U2 multivalue database and application development products (created by VMark, UniData, System Builder and Prime Computer, obtained via the Informix acquisition) to Rocket Software
April 2012 – IBM sells its Retail Store Solutions division (Point-of-Sales) to Toshiba TEC
January 2014 – IBM sells its IBM System x business to Lenovo for $2.3 billion.
October 2014 – IBM sells its Microelectronics (semiconductor) branch to GlobalFoundries. IBM will pay GlobalFoundries $1.5 billion over 3 years to take over the business.
December 2014 – UNICOM Global acquires IBM Rational Focal Point and IBM Rational Purify Plus.
January 2015 – IBM sells Algorithmics Collateral to SmartStream Technologies
December 2015 – UNICOM Global acquires IBM Rational System Architect
December 2018 – HCL Technologies to acquire Select IBM Software Products for $1.8B.
July 2019 – IBM Watson Marketing business spins off into standalone company Acoustic, after acquisition by Centerbridge Partners
October 8, 2020 – IBM announced it was spinning off the Managed Infrastructure Services unit of its Global Technology Services division into a new public company, an action expected to be completed by the end of 2021.
January 21, 2022 – IBM announced that it would sell Watson Health to the private equity firm Francisco Partners.
August 22, 2023 — IBM announced that the private equity firm Francisco Partners would acquire The Weather Company assets.
See also
List of largest mergers and acquisitions
Lists of corporate acquisitions and mergers
References
External links
IBM list of selected acquisitions
mergers and acquisitions
IBM | List of mergers and acquisitions by IBM | [
"Technology"
] | 2,161 | [
"Computing-related lists",
"IBM lists"
] |
5,716,217 | https://en.wikipedia.org/wiki/Greigite | Greigite is an iron sulfide mineral with the chemical formula . It is the sulfur equivalent of the iron oxide magnetite (Fe3O4). It was first described in 1964 for an occurrence in San Bernardino County, California, and named after the mineralogist and physical chemist Joseph W. Greig (1895–1977).
Natural occurrence and composition
It occurs in lacustrine sediments with clays, silts and arkosic sand often in varved sulfide rich clays. It is also found in hydrothermal veins. Greigite is formed by magnetotactic bacteria and sulfate-reducing bacteria. Greigite has also been identified in the sclerites of scaly-foot gastropods.
The mineral typically appears as microscopic (< 0.03 mm) isometric hexoctahedral crystals and as minute sooty masses. Association minerals include montmorillonite, chlorite, calcite, colemanite, veatchite, sphalerite, pyrite, marcasite, galena and dolomite.
Common impurities include Cu, Ni, Zn, Mn, Cr, Sb and As. Ni impurities are of particular interest because the structural similarity between Ni-doped greigite and the clusters present in biological enzymes has led to suggestions that greigite or similar minerals could have acted as catalysts for the origin of life. In particular, the cubic Fe4S4 unit of greigite is found in the Fe4S4 thiocubane units of proteins of relevance to the acetyl-CoA pathway.
Crystal structure
Greigite has the spinel structure. The crystallographic unit cell is cubic, with space group Fd3m. The S anions form a cubic close-packed lattice, and the Fe cations occupy both tetrahedral and octahedral sites.
Magnetic and electronic properties
Like the related oxide magnetite (Fe3O4), greigite is ferrimagnetic, with the spin magnetic moments of the Fe cations in the tetrahedral sites oriented in the opposite direction as those in the octahedral sites, and a net magnetization. It is a mixed-valence compound, featuring both Fe(II) and Fe(III) centers in a 1:2 ratio. Both metal sites have high spin quantum numbers. The electronic structure of greigite is that of a half metal.
References
Thiospinel group
Iron(II,III) minerals
Ferromagnetic materials
Magnetic minerals
Cubic minerals
Minerals in space group 227 | Greigite | [
"Physics"
] | 535 | [
"Materials",
"Ferromagnetic materials",
"Matter"
] |
5,716,325 | https://en.wikipedia.org/wiki/6LoWPAN | 6LoWPAN (acronym of "IPv6 over Low-Power Wireless Personal Area Networks") was a working group of the Internet Engineering Task Force (IETF).
It was created with the intention of applying the Internet Protocol (IP) even to the smallest devices, enabling low-power devices with limited processing capabilities to participate in the Internet of Things.
The 6LoWPAN group defined encapsulation, header compression, neighbor discovery and other mechanisms that allow IPv6 to operate over IEEE 802.15.4 based networks. Although IPv4 and IPv6 protocols do not generally care about the physical and MAC layers they operate over, the low-power devices and small packet size defined by IEEE 802.15.4 make it desirable to adapt to these layers.
The base specification developed by the 6LoWPAN IETF group is (updated by with header compression, with neighbor discovery optimization, with selective fragment recovery and with smaller changes in and ). The problem statement document is . IPv6 over Bluetooth Low Energy using 6LoWPAN techniques is described in .
Application areas
The targets for IPv6 networking for low-power radio communication are devices that need wireless connectivity to many other devices at lower data rates for devices with very limited power consumption. The header compression mechanisms in are used to allow IPv6 packets to travel over such networks.
IPv6 is also in use on the smart grid enabling smart meters and other devices to build a micro mesh network before sending the data back to the billing system using the IPv6 backbone. Some of these networks run over IEEE 802.15.4 radios, and therefore use the header compression and fragmentation as specified by RFC6282.
Thread
Thread is a standard from a group of more than fifty companies for a protocol running over 6LoWPAN to enable home automation. The specification is available at no cost , but paid membership is required to implement the protocol. Version 1.0 of the specification was published on 2015-10-29. The protocol will most directly compete with Z-Wave and Zigbee IP. In IoT device communications using the Matter standard, Thread is one of two possible wireless transport layers.
Functions
As with all link-layer mappings of IP, RFC4944 provides a number of functions. Beyond the usual differences between L2 and L3 networks, mapping from the IPv6 network to the IEEE 802.15.4 network poses additional design challenges (see for an overview).
Adapting the packet sizes of the two networks
IPv6 requires the link maximum transmission unit (MTU) to be at least 1280 octets. In contrast, IEEE 802.15.4's standard frame size is 127 octets. A maximum frame overhead of 25 octets and an optional but highly recommended security feature at the link layer poses an additional overhead of up to 21 octets are for AES-CCM-128. This leaves only 81 octets for the upper layers. Since this is so much less than 1280, 6LowPAN defines a fragmentation and reassembly layer. Further, the standard IPv6 Header is 40 octets long, so header compression is defined as well.
Address resolution
IPv6 nodes are assigned 128 bit IP addresses in a hierarchical manner, through an arbitrary length network prefix. IEEE 802.15.4 devices may use either of IEEE 64 bit extended addresses or, after an association event, 16 bit addresses that are unique within a PAN. There is also a PAN-ID for a group of physically collocated IEEE 802.15.4 devices.
Differing device designs
IEEE 802.15.4 devices are intentionally constrained in form factor to reduce costs (allowing for large-scale network of many devices), reduce power consumption (allowing battery powered devices) and allow flexibility of installation (e.g. small devices for body-worn networks). On the other hand, wired nodes in the IP domain are not constrained in this way; they can be larger and make use of mains power supplies.
Differing focus on parameter optimization
IPv6 nodes are geared towards attaining high speeds. Algorithms and protocols implemented at the higher layers such as TCP kernel of the TCP/IP are optimized to handle typical network problems such as congestion. In IEEE 802.15.4-compliant devices, energy conservation and code-size optimization remain at the top of the agenda.
Adaptation layer for interoperability and packet formats
An adaptation mechanism to allow interoperability between IPv6 domain and the IEEE 802.15.4 can best be viewed as a layer problem. Identifying the functionality of this layer and defining newer packet formats, if needed, is an enticing research area. proposes an adaptation layer to allow the transmission of IPv6 datagrams over IEEE 802.15.4 networks.
Addressing management mechanisms
The management of addresses for devices that communicate across the two dissimilar domains of IPv6 and IEEE 802.15.4 is cumbersome, if not exhaustingly complex.
Routing considerations and protocols for mesh topologies in 6LoWPAN
Routing per se is a two phased problem that is being considered for low-power IP networking:
Mesh routing in the personal area network (PAN) space.
The routability of packets between the IPv6 domain and the PAN domain.
Several routing protocols have been proposed by the 6LoWPAN community such as LOAD, DYMO-LOW, HI-LOW. However, only two routing protocols are currently legitimate for large-scale deployments: LOADng standardized by the ITU under the recommendation ITU-T G.9903 and RPL standardized by the IETF ROLL working group.
Device and service discovery
Since IP-enabled devices may require the formation of ad hoc networks, the current state of neighboring devices and the services hosted by such devices will need to be known. IPv6 neighbour discovery extensions is an internet draft proposed as a contribution in this area.
Security
IEEE 802.15.4 nodes can operate in either secure mode or non-secure mode. Two security modes are defined in the specification in order to achieve different security objectives: Access Control List (ACL) and Secure mode
See also
DASH7 active RFID standard
MyriaNed low-power, biology-inspired wireless technology
LoRaWAN allows low-bit-rate communication from and to connected objects, thus participating in Internet of Things, machine-to-machine (M2M), and smart city.
Thread (network protocol) standard suggested by Nest Labs based on IEEE 802.15.4 and 6LoWPAN
Static Context Header Compression (SCHC)
References
Further reading
Interoperability of 6LoWPAN
LowPan Neighbor Discovery Extensions
Serial forwarding approach to connecting TinyOS-based sensors to IPv6 Internet
GLoWBAL IPv6: An adaptive and transparent IPv6 integration in the Internet of Things Download
IETF Standardization in the Field of the Internet of Things (IoT): A Survey Download
External links
Internet Engineering Task Force (IETF)
6lowpan Working Group
6lowpan.tzi.org
IPv6
Wireless networking standards | 6LoWPAN | [
"Technology"
] | 1,436 | [
"Wireless networking",
"Wireless networking standards"
] |
5,716,492 | https://en.wikipedia.org/wiki/Blood%20type%20%28non-human%29 | Animal erythrocytes have cell surface antigens that undergo polymorphism and give rise to blood types. Antigens from the human ABO blood group system are also found in apes and Old World monkeys, and the types trace back to the origin of anthropoids. Other animal blood sometimes agglutinates (to varying levels of intensity) with human blood group reagents, but the structure of the blood group antigens in animals is not always identical to those typically found in humans. The classification of most animal blood groups therefore uses different blood typing systems to those used for classification of human blood.
Simian blood groups
Two categories of blood groups, human-type and simian-type, have been found in apes and monkeys, and they can be tested by methods established for grouping human blood. Data is available on blood groups of common chimpanzees, baboons, and macaques.
Rh blood group
The Rh system is named after the rhesus monkey, following experiments by Karl Landsteiner and Alexander S. Wiener, which showed that rabbits, when immunised with rhesus monkey red cells, produce an antibody that also agglutinates the red blood cells of many humans.
Chimpanzee and Old World monkey blood group systems
Two complex chimpanzee blood group systems, V-A-B-D and R-C-E-F systems, proved to be counterparts of the human MNS and Rh blood group systems, respectively.
Two blood group systems have been defined in Old World monkeys: the Drh system of macaques and the Bp system of baboons, both linked by at least one species shared by either of the blood group systems.
Canine blood groups
Over 13 canine blood groups have been described. Eight DEA (dog erythrocyte antigen) types are recognized as international standards. Of these DEA types, DEA 4 and DEA 6 appear on the red blood cells of ~98% of dogs. Dogs with only DEA 4 or DEA 6 can thus serve as blood donors for the majority of the canine population. Any of these DEA types may stimulate an immune response in a recipient of a blood transfusion, but reactions to DEA 1.1+ are the most severe.
Dogs that are DEA 1.1 positive (33 to 45% of the population) are universal recipients - that is, they can receive blood of any type without expectation of a life-threatening hemolytic transfusion reaction. Dogs that are DEA 1.1 negative are universal donors. Blood from DEA 1.1 positive dogs should never be transfused into DEA 1.1 negative dogs. If it is the dog's first transfusion the red cells transfused will have a shortened life due to the formation of alloantibodies to the cells themselves and the animal will forever be sensitized to DEA 1.1 positive blood. If it is a second such transfusion, life-threatening conditions will follow within hours. In addition, these alloantibodies will be present in a female dog's milk (colostrum) and adversely affect the health of DEA 1.1 negative puppies.
Other than DEA blood types, Dal is another blood type commonly known in dogs.
Feline blood groups
A majority of feline blood types are covered by the AB blood group, which designates cats as A, B, or AB. This type is determined by the CMAH alleles a cat possesses. The majority A allele seems to be dominant over the recessive B type, which is found with a higher frequency in some countries other than the United States. An "AB" type seems to be expressed by a third recessive allele. In a study conducted in England, 87.1% of non-pedigree cats were type A, while only 54.6% of pedigree cats were type A. Type A and B cats have naturally occurring alloantibodies to the opposite blood type, although the reaction of Type B cats to Type A blood is more severe than vice versa. Based on this, all cats should have a simple blood typing test done to determine their blood type prior to a transfusion or breeding to avoid haemolytic disease or neonatal isoerythrolysis.
An additional blood group system is Mik (+/-). It is only identified in 2007, with no specific gene mapped yet, but the prevalence of Mik- appears high enough for concern.
Equine blood groups
Horses have eight blood groups, of which seven, A, C, D, K, P, Q, and U, are internationally recognized, while the eighth, T, is primarily used in research. Each blood group has at least two allelic factors (for example, the A blood group has a, b, c, d, e, f, and g), which can be combined in all combinations (Aa, Afg, Abedg, etc.), to make many different alleles. This means that horses can have around 400,000 allelic combinations, allowing blood testing to be used as an accurate method of identifying a horse or determining parentage. Unlike humans, horses do not naturally produce antibodies against red blood cell antigens that they do not possess; this only occurs if they are somehow exposed to a different blood type, such as through blood transfusion or transplacental hemorrhage during parturition.
Breeding a mare to a stallion with a different blood type, usually Aa or Qa blood, risks neonatal isoerythrolysis if the foal inherits the blood type of the stallion. Group C is also of some degree of concern. This can also occur if a mare is bred to a jack, due to a "donkey factor". This immune-mediated disease is life-threatening and often requires transfusion.
Ideally, cross-matching should be performed prior to transfusion, or a universal donor may be used. The ideal universal whole blood donor is a non-thoroughbred gelding that is Aa, Ca, and Qa negative. If this is not available, a gelding, preferably of the same breed as the patient, may be used as a donor, and cross-matching may be crudely accessed by mixing donor serum with patient blood. If the mixture agglutinates, the donor blood contains antibodies against the blood of the patient, and should not be used.
Bovid blood groups
The polymorphic systems in cattle include the A, B, C, F, J, L, M, S, and Z polymorphisms.
Sheep blood types are A, B, C, D, M, R and X. The B system is highly polymorphic. The R system is soluble. The M-L system is involved in active red cell potassium transport and polymorphisms.
In goats there are A, B, C, M and J, similar to sheep.
Birds
In parrots, notably, there are no reported blood types, but there is a better success rate of transfusion between same species of animal.
In chickens, the blood groups are A, B, C, D, E, H, I, J, K, L, N, P, and R.
References
Further reading
External links
H/h blood groups in non-humans at BGMUT Blood Group Antigen Gene Mutation Database at NCBI, NIH
MNS blood groups in non-humans at BGMUT Blood Group Antigen Gene Mutation Database at NCBI, NIH
Rh blood groups in non-humans at BGMUT Blood Group Antigen Gene Mutation Database at NCBI, NIH
Animal physiology | Blood type (non-human) | [
"Biology"
] | 1,564 | [
"Animals",
"Animal physiology"
] |
5,717,312 | https://en.wikipedia.org/wiki/Maze%20runner | In electronic design automation, maze runner is a connection routing method that represents the entire routing space as a grid. Parts of this grid are blocked by components, specialised areas, or already present wiring. The grid size corresponds to the wiring pitch of the area. The goal is to find a chain of grid cells that go from point A to point B.
A maze runner may use the Lee algorithm. It uses a wave propagation style (a wave are all cells that can be reached in n steps) throughout the routing space. The wave stops when the target is reached, and the path is determined by backtracking through the cells.
See also
Autorouter
References
. One of the first descriptions of a maze router.
Electronic engineering
Electronic design automation
Electronics optimization | Maze runner | [
"Technology",
"Engineering"
] | 153 | [
"Electrical engineering",
"Electronic engineering",
"Computer engineering"
] |
5,717,580 | https://en.wikipedia.org/wiki/Active%20appearance%20model | An active appearance model (AAM) is a computer vision algorithm for matching a statistical model of object shape and appearance to a new image. They are built during a training phase. A set of images, together with coordinates of landmarks that appear in all of the images, is provided to the training supervisor.
The model was first introduced by Edwards, Cootes and Taylor in the context of face analysis at the 3rd International Conference on Face and Gesture Recognition, 1998. Cootes, Edwards and Taylor further described the approach as a general method in computer vision at the European Conference on Computer Vision in the same year. The approach is widely used for matching and tracking faces and for medical image interpretation.
The algorithm uses the difference between the current estimate of appearance and the target image to drive an optimization process.
By taking advantage of the least squares techniques, it can match to new images very swiftly.
It is related to the active shape model (ASM). One disadvantage of ASM is that it only uses shape constraints (together with some information about the image structure near the landmarks), and does not take advantage of all the available information – the texture across the target object. This can be modelled using an AAM.
References
Some reading
T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham. Training models of shape from sets of examples. In Proceedings of BMVC'92, pages 266–275, 1992
S. C. Mitchell, J. G. Bosch, B. P. F. Lelieveldt, R. J. van der Geest, J. H. C. Reiber, and M. Sonka. 3-d active appearance models: Segmentation of cardiac MR and ultrasound images. IEEE Trans. Med. Imaging, 21(9):1167–1178, 2002
T.F. Cootes, G. J. Edwards, and C. J. Taylor. Active appearance models. ECCV, 2:484–498, 1998[pdf]
External links
Professor Tim Cootes AAM Code Free Tools for experimenting with AAMs from Manchester University (for research use only).
Professor Tim Cootes AAM Page Co-creator of AAM page from Manchester University.
IMM AAM Code Dr Mikkel B. Stegmann's home page of AAM-API, C++ AAM implementation (non-commercial use only).
Matlab AAM Code Open-source Matlab implementation of the original AAM algorithm.
AAMtools An Active Appearance Modelling Toolbox in Matlab by Dr George Papandreou.
DeMoLib AAM Toolbox in C++ by Dr Jason Saragih and Dr Roland Goecke.
Computer vision | Active appearance model | [
"Engineering"
] | 569 | [
"Artificial intelligence engineering",
"Packaging machinery",
"Computer vision"
] |
5,718,055 | https://en.wikipedia.org/wiki/Project%20West%20Ford | Project West Ford (also known as Westford Needles and Project Needles) was a test carried out by Massachusetts Institute of Technology's Lincoln Laboratory on behalf of the United States military in 1961 and 1963 to create an artificial ionosphere above the Earth. This was done to solve a major weakness that had been identified in military communications.
History
At the height of the Cold War, all international communications were either sent through submarine communications cables or bounced off the natural ionosphere. The United States military was concerned that the Soviets might cut those cables, forcing the unpredictable ionosphere to be the only means of communication with overseas forces.
To mitigate the potential threat, Walter E. Morrow started Project Needles at the MIT Lincoln Laboratory in 1958. The goal of the project was to place a ring of 480,000,000 copper dipole antennas in orbit to facilitate global radio communication. The dipoles collectively provided passive support to Project West Ford's parabolic dish (located at the Haystack Observatory in the town of Westford) to communicate with distant sites.
The needles used in the experiment were long and [1961] or [1963] in diameter. The length was chosen because it was half the wavelength of the 8 GHz signal used in the study. The needles were placed in medium Earth orbit at an altitude of between at inclinations of 96 and 87 degrees.
A first attempt was launched on 21 October 1961, during which the needles failed to disperse. The project was eventually successful with the 9 May 1963 launch, with radio transmissions carried by the manufactured ring. However, the technology was ultimately shelved, partially due to the development of the modern communications satellite and partially due to protests from other scientists.
British radio astronomers, optical astronomers, and the Royal Astronomical Society protested the experiment. The Soviet newspaper Pravda also joined the protests under the headline "U.S.A. Dirties Space". The International Academy of Astronautics regards the experiment as the worst deliberate release of space debris.
At the time, the issue was raised in the United Nations where the then United States Ambassador to the United Nations Adlai Stevenson defended the project. Stevenson studied the published journal articles on Project West Ford. Using what he learned on the subject and citing the articles he had read, he successfully allayed the fears of most UN ambassadors from other countries. He and the articles explained that sunlight pressure would cause the dipoles to only remain in orbit for a short period of approximately three years. The international protest ultimately resulted in a consultation provision included in the 1967 Outer Space Treaty.
Although the dispersed needles in the second experiment removed themselves from orbit within a few years, some of the dipoles that had not deployed correctly remained in clumps, contributing a small amount of the orbital debris tracked by NASA's Orbital Debris Program Office. Their numbers have been diminishing over time as they occasionally re-enter. , 44 clumps of needles larger than 10 cm were still known to be in orbit.
Launches
References
Space debris
Satellites of the United States
1961 in the United States
1961 in science
1962 in the United States
1962 in science
1963 in the United States
1963 in science
Military projects of the United States
1961 in spaceflight
1962 in spaceflight
1963 in spaceflight | Project West Ford | [
"Technology",
"Engineering"
] | 648 | [
"Military projects of the United States",
"Military projects",
"Space debris"
] |
5,718,367 | https://en.wikipedia.org/wiki/Oleanane | Oleanane is a natural triterpenoid. It is commonly found in woody angiosperms and as a result is often used as an indicator of these plants in the fossil record. It is a member of the oleanoid series, which consists of pentacyclic triterpenoids (such as beta-amyrin and taraxerol) where all rings are six-membered.
Structure
Oleanane is a pentacyclic triterpenoid, a class of molecules made up of six connected isoprene units. The naming of both the ring structures and individual carbon atoms in oleanane is the same as in steroids. As such, it consists of a A, B, C, D, and E ring, all of which are six-membered rings.
The structure of oleanane contains a number of different methyl groups, that vary in orientation between different oleananes. For example, in 18-alpha-oleanane contains a downward facing methyl group for the 18th carbon atom, while 18-beta-oleanane contains an upward facing methyl group at the same position.
A and B rings of the oleanane structure are identical to that of hopane. As a result, both molecules produce a fragment of m/z 191. Because this fragment is often used to identify hopanes, oleanane can be mis-identified in hopane analysis.
Synthesis
Like other triterpenoids, are formed from six combined isoprene units. These isoprene units can be combined via a number of different pathways. In eukaryotes (including plants), this pathway is the mevalonate (MVA) pathway. For the formation of steroids and other triterpenoids the isoprenoids are combined into a precursor known as squalene, which then undergoes enzymatic cyclization to produce the various different triterpenoids, including oleanane.
Once the oleananes have been transported into rocks or sediments they will undergo further alteration before they are measured.
Measurement in Rock Samples
Oleananes can be identified in extracts from rock samples (or plants) using GC/MS. A GC/MS is a gas chromatograph coupled with a mass spectrometer. The sample is first injected into the system, then run through as chromatographic column. How fast a material moves through a chromatographic column depends on how long it spends in each of the two stages there. Compounds that partition more into the mobile phase will move faster as opposed to compounds that partition more into the stationary phase. The result of this is a separation of different organic molecules based on their retention time in the GC.
After being separated by the GC, the compounds can then be analyzed by a mass spectrometer. Each compound will contain a characteristic mass spectrum, based on the fragments it splits into during ionization in the mass spectrometer. This means that the GC can not only separate different types of molecules, it can also identify them.
As mentioned above, they have a characteristic mass fragment at m/z = 191, and thus will appear in the same selected ion chromatograph (SIC) as hopanes. This can help one identify them in GC/MS datasets.
Uses
As a biomarker
Oleanane has been identified as a compound in modern day angiosperms.
Because of this, its presence is the fossil record has also been used to trace angiosperms through the fossil record. For example, the ratio of 18-alpha-oleanane + 18-beta-oleanane:17-alpha-hopane in rock extracts (and associated petroleums/oils) has been found to correlate (at least broadly) to the presence of angiosperms in the fossil record. In this study, the combination of alpha and beta-oleanane were used as indicators for the presence of angiosperms. They are normalized to hopanes, which are broadly present in almost all rock extracts coming from petroleum. Furthermore, because of the structural similarities between hopanes and oleananes, it is assumed that they will react similarly to the various weathering processes that degrade the biomarkers present. As such, the ratio of hopanes to oleananes should be similar to the initial ratio, and unaffected by processes occurring in the rock after fossilization.
There is some delay in the accepted increases in taxonomic diversification of angiosperms (which occurred during the mid-Cretaceous period) and the increase of oleanane concentrations in the fossil record (which occurred in the late-Cretaceous or even after). This could be due to a number of factors, one being that the early angiosperms were more herbaceous than woody and that woody angiosperms only appeared after further taxonomic diversification.
Lastly, the study introduced the idea of an "oleanane parameter," which could be used in assessing angiosperm input to petroleum sources. This, in turn, gives some idea of the age of said petroleum sources.
That being said, the presence of angiosperms may not be the only thing affecting the oleanane content of sediments, rock extracts and petroleum. For example, there is evidence that contact with seawater during early sedimentation processes can increase the concentration of oleananes in the mature sediment. This evidence comes from the fact that various indicators of marine influence (C27/C29 sterane ratios, changes in elemental composition in the downstream direction that are indicative of the infiltration of water into the system and the homophane index). Despite this, it is still unclear as to how marine influence enhances the expression of oleananes (thus increasing observed concentration). Some ideas include the changes in pH, Eh and the microbial environment that come with the interaction with seawater.
See also
Oleanolic acid
References
Triterpenes
Polycyclic nonaromatic hydrocarbons
Biomarkers | Oleanane | [
"Biology"
] | 1,233 | [
"Biomarkers"
] |
5,718,732 | https://en.wikipedia.org/wiki/R%C3%A9union%20swamphen | The Réunion swamphen (Porphyrio caerulescens), also known as the Réunion gallinule or (French for "blue bird"), is a hypothetical extinct species of rail that was endemic to the Mascarene island of Réunion. While only known from 17th- and 18th-century accounts by visitors to the island, it was scientifically named in 1848, based on the 1674 account by Sieur Dubois. A considerable literature was subsequently devoted to its possible affinities, with current researchers agreeing it was derived from the swamphen genus Porphyrio. It has been considered mysterious and enigmatic due to the lack of any physical evidence of its existence.
This bird was described as entirely blue in plumage with a red beak and legs. It was said to be the size of a Réunion ibis or chicken, which could mean in length, and it may have been similar to the takahē. While easily hunted, it was a fast runner and able to fly, though it did so reluctantly. It may have fed on plant matter and invertebrates, as do other swamphens, and was said to nest among grasses and aquatic ferns. It was only found on the Plaine des Cafres plateau, to which it may have retreated during the latter part of its existence, whereas other swamphens inhabit lowland swamps. While the last unequivocal account is from 1730, it may have survived until 1763, but overhunting and the introduction of cats likely drove it to extinction.
Taxonomy
Visitors to the Mascarene island of Réunion during the 17th and 18th centuries reported blue birds ( in French). The first such account is that of the French traveller Sieur Dubois, who was on Réunion from 1669 to 1672, which was published in 1674. The British naturalist Hugh Edwin Strickland stated in 1848 that he would have thought Dubois' account referred to a member of the swamphen genus Porphyrio if not for its large size and other features (and noted the term had also been erroneously used for bats on Réunion in an old account). Strickland expressed hope that remains of this and other extinct Mascarene birds would be found there. Responding to Strickland's book later that year, the Belgian scientist Edmond de Sélys Longchamps coined the scientific name Apterornis coerulescens based on Dubois' account. The specific name is Latin for "bluish, becoming blue". Sélys Longchamps also included two other Mascarene birds, at the time only known from contemporary accounts, in the genus Apterornis: the Réunion ibis (now Threskiornis solitarius); and the red rail (now Aphanapteryx bonasia). He thought them related to the dodo and Rodrigues solitaire, due to their shared rudimentary wings, tail, and the disposition of their digits.
The name Apterornis had already been used for a different extinct bird genus from New Zealand (originally spelled Aptornis, the adzebills) by the British biologist Richard Owen earlier in 1848, and the French biologist Charles Lucien Bonaparte coined the new binomial Cyanornis erythrorhynchus for the in 1857. The same year, the German ornithologist Hermann Schlegel moved the species to the genus Porphyrio, as P. (Notornis) caerulescens, indicating an affinity with the takahē (now called Porphyrio hochstetteri, then also referred to as Notornis by some authors) of New Zealand. Schlegel argued that the discovery of the takahē showed that members of Porphyrio could be large, thereby disproving Strickland's earlier doubts based on size. The British ornithologist Richard Bowdler Sharpe simply used the name Porphyrio caerulescens in 1894. The British zoologist Walter Rothschild retained the name Apterornis for the bird in 1907, and considered it similar to Aptornis and the takahē, believing Dubois's account indicated it was related to those birds. The Japanese ornithologist Masauji Hachisuka used the new combination Cyanornis coerulescens for the bird in 1953 (with the specific name misspelled), also considering it related to the takahē due to its size.
Throughout the 20th century the bird was usually considered a member of Porphyrio or Notornis, and the latter genus was eventually itself considered a junior synonym of Porphyrio. Some writers equated the bird with extant swamphens, including African swamphens by the French ornithologist Jacques Berlioz in 1946, and western swamphens by the French ornithologist Nicolas Barré in 1996, despite their different habitat. The French ornithologist Philippe Milon doubted the Porphyrio affiliation in 1951, since Dubois's account stated the Réunion bird was palatable, while extant swamphens are not. In 1967, the American ornithologist James Greenway stated that the bird "must remain mysterious" until Porphyrio bones are one day uncovered.
In 1974, an attempt was made to find fossil localities on the Plaine des Cafres plateau, where the bird was said to have lived. No caves, which might contain kitchen middens where early settlers discarded bones of local birds, were found, and it was determined that a more careful study of the area was needed before excavations could be made. In 1977, the American ornithologist Storrs L. Olson found the old accounts consistent with an endemic derivative of Porphyrio, and considered it a probable species whose remains might one day be discovered. The British ecologist Anthony S. Cheke considered previous arguments about the bird's affinities in 1987, and supported it being a Porphyrio relative, while noting that there were two further contemporary accounts. The same year, the British writer Errol Fuller listed the bird as a hypothetical species, and expressed puzzlement as to how a considerable literature had been derived from such "flimsy material".
The French palaeontologist Cécile Mourer-Chauviré and colleagues listed the bird as Cyanornis (?=Porphyrio) caerulescens in 2006, indicating the uncertainty of its classification. They stated the cause of the scarcity of its fossil remains was probably that it did not live in the parts of Réunion where fossils might have been preserved. Cheke and the British palaeontologist Julian P. Hume stated in 2008 that, since the mystery of the "Réunion solitaire" had been solved after it was identified with ibis remains, the Réunion swamphen remains the most enigmatic of the Mascarene birds from the old accounts. In his 2012 book about extinct birds and his 2019 monograph about extinct Mascarene rails, Hume stated that the Réunion swamphen had been mentioned by trustworthy observers, but was "perhaps the most enigmatic of all rails" with no evidence to resolve its taxonomy. He thought there was no doubt that it was a derivative of Porphyrio, as the all-blue colouration is only found in that genus among rails. While it may have been derived from Africa or Madagascar, genetic studies have shown that other rails have dispersed to unexpectedly great distances from their closest relatives, making alternative explanations possible.
Description
The Réunion swamphen was described as having entirely blue plumage with a red beak and legs, and is generally agreed to have been a large, terrestrial swamphen, with features indicative of reduced flight capability, such as larger size and more robust legs. There has been disagreement over the size of the bird, as Dubois' account compared its size with that of a Réunion ibis while that of the French engineer Jean Feuilley from 1704 compared it to a domestic chicken. Cheke stated in 1987 that Feuilley's account would indicate the bird was not unusually large, perhaps the size of a swamphen. Hume pointed out in 2019 that the Réunion ibis would have been at most, similar to the extant African sacred ibis (including the tail), while chickens could be in length (the size of their ancestor, the wild red junglefowl), and there was therefore no contradiction. The Réunion swamphen would thereby have been about the same size as the takahē.
The first description of the Réunion swamphen is that of Dubois from 1674:
The last definite account of the bird is that of the priest Father Brown from around 1730 (expanded from a 1717 account by Le Gentil):
Olson stated the comparison to a "wood pigeon" was a reference to the common wood pigeon, implying that Brown described it as smaller than Dubois did, while Hume suggested it could be the extinct Réunion blue pigeon. The 1708 account of Hébert does not add much information, though he qualified its colouration as "dark blue".
While the bird is only known from written accounts, reconstructions of it appear in Rothschild's 1907 book Extinct Birds, and Hachisuka's 1953 book The Dodo and Kindred Birds. Rothschild stated he had the Dutch artist John Gerrard Keulemans depict it as intermediate between the takahē and Aptornis, which he thought its closest relatives. Fuller found Frohawk's illustration to be a well-produced work, though almost entirely conjectural in depicting it like a slimmed-down takahē.
Behaviour and ecology
Little is known about the ecology of the Réunion swamphen; it was easily caught and killed, unlike other swamphens (which avoid predators by flying or hiding), though it was able to run fast. While some early researchers thought the bird to be flightless, Brown's account states it could fly, and it is thought to have been a reluctant flier. Hume suggested it may have fed on plant matter and invertebrates, as other swamphens do. At least in the latter part of its existence, it appears to have been confined to mountains (retreating there between the 1670s and 1705), in particular to the Plaine des Cafres plateau, situated at an altitude of about in south-central Réunion. The environment of this area consists of open woodland in a subalpine forest steppe, and has marshy pools.
The Réunion swamphen was termed a land-bird by Dubois, while other swamphens inhabit lowland swamps. This is similar to the Réunion ibis, which lived in forest rather than wetlands, which is otherwise typical ibis habitat. Cheke and Hume proposed that the ancestors of these birds colonised Réunion before swamps had developed, and had therefore become adapted to the available habitats. They were perhaps prevented from colonising Mauritius as well due to the presence of red rails there, which may have occupied a similar ecological niche.
Feuilley described some characteristics of the bird in 1704:
The only account of its nesting behaviour is that of La Roque from 1708:
Many other endemic species on Réunion became extinct after the arrival of humans and the resulting disruption of the island's ecosystem. The Réunion swamphen lived alongside other now-extinct birds, such as the Réunion ibis, the Mascarene parrot, the Hoopoe starling, the Réunion parakeet, the Réunion scops owl, the Réunion night heron, and the Réunion pink pigeon. Extinct Réunion reptiles include the Réunion giant tortoise and an undescribed Leiolopisma skink. The small Mauritian flying fox and the snail Tropidophora carinata lived on Réunion and Mauritius before vanishing from both islands.
Extinction
Many terrestrial rails are flightless, and island populations are particularly vulnerable to man-made changes; as a result, rails have suffered more extinctions than any other family of birds. All six endemic species of Mascarene rails are extinct, all caused by human activities. Overhunting was the main cause of the Réunion swamphen's extinction (it was considered good game and was easy to catch), but according to Cheke and Hume, the introduction of cats at the end of the 17th century could have contributed to the elimination of the bird once these became feral and reached its habitat. Today, cats are still a serious threat to native birds, in particular Barau's petrel, since they occur all over Réunion, including the most remote and high peaks. The eggs and chicks would also have been vulnerable to rats after their accidental introduction in 1676. On the other hand, the Réunion swamphen and other birds of the island appear to have successfully survived feral pigs. Cattle grazing on Plaine des Cafres was promoted by the French explorer Jean-Baptiste Charles Bouvet de Lozier in the 1750s, which may have also had an impact on the bird.
While the last unequivocal account of the Réunion swamphen is from 1730, an anonymous account from 1763, possibly by the British Brigadier-General Richard Smith, may be the last mention of this bird, though no description of it was provided, and it might refer to another species. It is also impossible to say whether this writer saw the bird himself. It gives a contemporary impression of the Réunion swamphen's habitat, Plaine des Cafres, and of how birds were hunted there:
If the Réunion swamphen survived until 1763 this would be far longer than many other extinct birds of Réunion. If so, its survival was likely because of the remoteness of its habitat.
See also
List of extinct animals of Réunion
References
Extinct birds of Indian Ocean islands
Porphyrio
Bird extinctions since 1500
Birds of Réunion
†
Birds described in 1848
Hypothetical species | Réunion swamphen | [
"Biology"
] | 2,773 | [
"Biological hypotheses",
"Controversial taxa",
"Hypothetical species"
] |
5,718,793 | https://en.wikipedia.org/wiki/ORiNOCO | ORiNOCO was the brand name for a family of wireless networking technology by Proxim Wireless (previously Lucent). These integrated circuits (codenamed Hermes) provide wireless connectivity for 802.11-compliant Wireless LANs.
Variants
Lucent offered several variants of the PC Card, referred to by different color-based monikers:
White/Bronze: WaveLAN IEEE Standard 2 Mbit/s PC Cards with 802.11 support.
Silver: WaveLAN IEEE Turbo 11 Mbit/s PC Cards with 802.11b and 64-bit WEP support.
Gold: WaveLAN IEEE Turbo 11 Mbit/s PC Cards with 802.11b and 128-bit WEP support.
Later models dropped the 'Turbo' moniker due to 802.11b 11 Mbit/s becoming widespread.
Proxim, after taking over Lucent's wireless division, rebranded all their wireless cards to ORiNOCO - even cards not based on Lucent/Agere's Hermes chipset. Proxim still offers ORiNOCO-based cards under the 'Classic' brand.
Rebranded products
The WaveLAN chipsets that power ORiNOCO-branded cards were commonly used to power other wireless networking devices, and are compatible with a number of other access points, routers and wireless cards. The following brand and models utilise the chipset, or are rebrands of an ORiNOCO product:
3Com AirConnect
Apple AirPort and AirMac cards (original only, not AirPort Extreme). Modified to remove the antenna stub.
AVAYA World Card
Cabletron RoamAbout 802.11 DS
Compaq WL100 11 Mbit/s Wireless Adapter
D-Link DWL-650
ELSA AirLancer MC-11
Enterasys RoamAbout
Ericsson WLAN Card C11
Farallon SkyLINE
Fujitsu RoomWave
HyperLink Wireless PC Card 11 Mbit/s
Intel PRO/Wireless 2011
Lucent Technologies WaveLAN/IEEE Orinoco
Melco WLI-PCM-L11
Microsoft Wireless Notebook Adapter MN-520
NCR WaveLAN/IEEE Adapter
Proxim LAN PC CARD HARMONY 80211B
Samsung 11 Mbit/s WLAN Card
Symbol LA4111 Spectrum24 Wireless LAN PC Card
Toshiba Wireless LAN Mini PCI Card
Preferred wireless chipset for wardriving
The ORiNOCO (and their derivatives) is preferred by wardrivers, due to their high sensitivity and the ability to report the level of noise (something that other chips do not report). The pre-Proxim (or 'Classic') ORiNOCO cards have a jack for attaching an external antenna.
Linux drivers
A Linux Orinoco Driver supported the IEEE 802.11b Hermes/ORiNOCO family of chips. It was included in the Linux kernel from version 2.4.3 until its removal in 6.8
External links
MPL/GPL drivers
Proxim Website for ORiNOCO
ORiNOCO AP-8100
References
Wireless networking hardware | ORiNOCO | [
"Technology"
] | 615 | [
"Wireless networking hardware",
"Wireless networking"
] |
5,718,913 | https://en.wikipedia.org/wiki/WaveLAN | WaveLAN was a brand name for a family of wireless networking technology sold by NCR, AT&T, Lucent Technologies, and Agere Systems as well as being sold by other companies under OEM agreements. The WaveLAN name debuted on the market in 1990 and was in use until 2000, when Agere Systems renamed their products to ORiNOCO. WaveLAN laid the important foundation for the formation of IEEE 802.11 working group and the resultant creation of Wi-Fi.
WaveLAN has been used on two different families of wireless technology:
Pre-IEEE 802.11 WaveLAN, also called Classic WaveLAN
IEEE 802.11-compliant WaveLAN, also known as WaveLAN IEEE and ORiNOCO
History
WaveLAN was originally designed by NCR Systems Engineering, later renamed into WCND (Wireless Communication and Networking Division) at Nieuwegein, in the province Utrecht in the Netherlands, a subsidiary of NCR Corporation, in 1986–7, and introduced to the market in 1990 as a wireless alternative to Ethernet and Token Ring. The next year NCR contributed the WaveLAN design to the IEEE 802 LAN/MAN Standards Committee. This led to the founding of the 802.11 Wireless LAN Working Committee which produced the original IEEE 802.11 standard, which eventually became the basis of the certification mark Wi-Fi. When NCR was acquired by AT&T in 1991, becoming the AT&T GIS (Global Information Solutions) business unit, the product name was retained, as happened two years later when the product was transferred to the AT&T GBCS (Global Business Communications Systems) business unit, and again when AT&T spun off their GBCS business unit as Lucent in 1995. The technology was also sold as WaveLAN under an OEM agreement by Epson, Hitachi, and NEC, and as the RoamAbout DS by DEC. It competed directly with Aironet's non-802.11 ARLAN lineup, which offered similar speeds, frequency ranges and hardware.
Several companies also marketed wireless bridges and routers based on the WaveLAN ISA and PC cards, like the C-Spec OverLAN, KarlNet KarlBridge, Persoft Intersect Remote Bridge, and Solectek AIRLAN/Bridge Plus. Lucent's WavePoint II access point could accommodate both the classic WaveLAN PC cards as well as the WaveLAN IEEE cards. Also, there were a number of compatible third-party products available to address niche markets such as: Digital Ocean's Grouper, Manta, and Starfish offerings for the Apple Newton and Macintosh; Solectek's 915 MHz WaveLAN parallel port adapter; Microplex's M204 WaveLAN-compatible wireless print server; NEC's Japanese-market only C&C-Net 2.4 GHz adapter for the NEC-bus; Toshiba's Japanese-market only WaveCOM 2.4 GHz adapter for the Toshiba-Bus; and Teklogix's WaveLAN-compatible Pen-based and Notebook terminals.
During this time frame, networking professionals also realized that since NetWare 3.x and 4.x supported the WaveLAN cards and came with a Multi Protocol Router module that supported the IP/IPX RIP and OSPF routing protocols, one could construct a wireless routed network using NetWare servers and WaveLAN cards for a fraction of the cost of building a wireless bridged network using WaveLAN access points. Many NetWare classes and textbooks of the time included a NetWare OS CD with a 2-person license, so potentially the only cost incurred came from hardware.
When the 802.11 protocol was ratified, Lucent began producing chipsets and PC-cards to support this new standard under the name of WaveLAN IEEE. WaveLAN was among the first products certified by the Wi-Fi Alliance, originally called the Wireless Ethernet Compatibility Association (WECA). Shortly thereafter, Lucent spun off its semiconductor division that also produced the WaveLAN chipsets as Agere Systems. On June 17, 2002 Proxim acquired the IEEE 802.11 LAN equipment business including the trademark ORiNOCO from Agere Systems. Proxim later renamed its entire 802.11 wireless networking lineup to ORiNOCO, including products based on Atheros chipsets.
Specifications
Classic WaveLAN operates in the 900 MHz or 2.4 GHz ISM bands. Being a proprietary pre-802.11 protocol, it is completely incompatible with the 802.11 standard. Soon after the publication of the IEEE 802.11 standard on November 18, 1997, WaveLAN IEEE was placed on the market.
Hardware
The pre-802.11 standard WaveLAN cards were based on the Intel 82586 Ethernet PHY controller, which was a commonly used controller in its time and was found in many ISA and MCA Ethernet cards, such as the Intel EtherExpress 16 and the 3COM 3C523. The WaveLAN IEEE ISA, MCA and PCMCIA cards used Medium Access Controller (MAC), HERMES, designed specifically for 802.11 protocol support. The radio modem section was hidden from the OS, thus making the WaveLAN card appear to be a typical Ethernet card, with the radio-specific features taken care of behind the scenes.
While the 900 MHz models and the early 2.4 GHz models operated on one fixed frequency, the later 2.4 GHz cards as well as some 2.4 GHz WavePoint access points had the hardware capacity to operate over ten channels, ranging from 2.412 GHz to 2.484 GHz, with the channels available being determined by the region-specific firmware.
Security
For security, WaveLAN used a 16-bit NWID (NetWork ID) field, which yielded 65,536 potential combinations; the radio portion of the device could receive radio traffic tagged with another NWID, but the controller would discard the traffic. DES encryption (56-bit) was an option in some of the ISA and MCA cards and all of the WavePoint access points. The full-length ISA and MCA cards had a socket for an encryption chip, the half-length 915 MHz ISA cards had solder pads for a socket which was never added, and the 2.4 GHz half-length ISA cards had the chip soldered directly to the board.
For the IEEE 802.11 standard the goal was to provide data confidentiality comparable to that of a traditional wired network, using 64- and 128-bit data encryption technology. This first implementation was called “Wired Equivalent Privacy” (WEP).
There are shortcomings in WaveLAN & initial 802.11 compatible devices security strategy:
The initial IEEE 802.11 security WEP implementation, was shown to be vulnerable to attack.
This was addressed by the 802.11i Wi-Fi Protected Access (WPA) that replaced WEP in the standard.
Official specifications
Support
Officially released drivers
Windows 3.11, 95, and NT 3.5/4.0
Windows 3.11, Windows 95, and 98 supported the ISA and MCA cards natively but did not provide any configuration or link diagnostics utilities.
Windows NT 3.51 did not natively support the WaveLAN cards, but additional drivers from Microsoft's Windows NT Driver Library were available.
OS/2 NDIS and NetWare Requester
LAN Manager/IBM LAN Server
Artisoft LANtastic
PC-TCP for DOS
NetWare Lite, NetWare 2, 3, and 4. Netware 4.11 through 5.x supported the ISA and MCA cards natively but did not provide any configuration or link diagnostics utilities.
ODI/VLM NetWare client for DOS. The DOS drivers came with configuration and link diagnostics utilities.
SCO UNIX version 1.00.00.00
UnixWare version 1.1
NCR's documentation stated that drivers for Banyan Vines 5.05 were available on Banyan's BBS, but it is unclear if they ever materialized
Volunteer-developed drivers
Linux has included support for ISA Classic WaveLAN cards since the 2.0.37 kernel, while full support for the PC card Classic WaveLAN cards came later. Status of support for MCA Classic Wavelan cards is unknown.
FreeBSD version 2.2.1-up and the Mach4 kernel have had native support for the ISA Classic WaveLAN cards for several years. OpenBSD and NetBSD do not natively support any of the Classic WaveLAN cards.
Several open-source projects, such as NdisWrapper and Project Evil, currently exist that allow the use of NDIS drivers via a "wrapper". This allows non-Windows OS' to utilize the near-universal nature of drivers written for the Windows platform to the benefit of other operating systems, such as Linux, FreeBSD, and ZETA.
Examples
Classic WaveLAN technology was available for the MCA, ISA/EISA, and PCMCIA interfaces:
915 MHz
Full-length ISA card
F connector
RG-59/U antenna cable
NCR 008-0126998 HOLI (HOst Lan Interface) chip
NCR 008-0126999 Icarus or NCR 008-0127211 Daedalus chip
Intel N82586 PHY controller chip
IRQ, boot ROM, and boot ROM base address configured with a four-position DIP switch block at top of card
NCR part number 601-0068991
AT&T part number 3399-F170
Half-length ISA card
SMB connector
NCR 008-0126998 HOLI chip
Intel N82586 PHY controller chip
IRQ, boot ROM, and boot ROM base address configured with a four-position DIP switch block at top of card
AT&T part number 3399-K602.
Full-length MCA card
F connector
NCR 008-0127216 HOLI chip
NCR 008-0126999 Icarus chip
NCR 8-127000A socketed DES encryption chip
Intel N82586 PHY controller chip
MCA id number 6A14.
PC card
Large EAM (External Antenna Module)
Intel i82593 PHY controller chip
AT&T part number 3399-K080
Compaq/DEC Roamabout part number: DEINA-AA.
2.4 GHz
Full-length ISA card
Fixed frequency
IRQ, boot ROM, and boot ROM base address configured with a four-position DIP switch block at top of card
Half-length ISA card
SMB connector
Selectable frequency
Symbios Logic 008-0126998 HOLI chip
Intel N82586 PHY controller chip
IRQ, boot ROM, and boot ROM base address configured with a four-position DIP switch block at top of card
AT&T part number 3399-K635.
Full-length MCA card
SMB connector
NCR 008-0127216 HOLI chip
NCR 008-0127211 Daedalus chip
NCR 8-127000A socketed DES encryption chip
Intel N82586 PHY controller chip
AT&T part number 3399-K066
MCA id number 6A14.
PC card - 2.4 GHz, selectable frequency, large EAM (External Antenna Module).
Intel N82593 PHY controller chip
AT&T part number: AT&T 3399-K624.
Lucent part number: LUC 3399-K644.
Compaq/DEC Roamabout part number: DEIRB-xx.
Options
DES encryption chip. Part number 3399-K972.
Boot ROM chip. Part number 3399-K973.
Citations
References
NCR WaveLAN PC-AT Installation and Operations manual, part number ST-2119-09, revision number 008-0127167 Rev. B, copyright 1990, 1991 by NCR Corporation.
External links
NCR's HTTP site with a selection of WaveLAN drivers and documentation
FTP mirror site of DEC's ftp server with a selection of RoamAbout drivers and documentation
Detailed analysis of WaveLAN ISA cards
Wayback machine archive of documentation on an NCR WaveLAN backbone built in Latvia
Wayback machine archive of Byte Magazine's review of WaveLAN
Wayback machine archive for Wavelan Classic products
Detailed analysis of Wavelan MCA cards
Wireless networking
Network access
NCR Corporation products | WaveLAN | [
"Technology",
"Engineering"
] | 2,535 | [
"Electronic engineering",
"Wireless networking",
"Network access",
"Computer networks engineering"
] |
5,719,215 | https://en.wikipedia.org/wiki/Aggressive%20driving | Aggressive driving is defined by the National Highway Traffic Safety Administration as the behaviour of an individual who "commits a combination of moving traffic offences so as to endanger other persons or property."
Definitions
In the UK, Road Drivers offers a basic definition of aggressive driving:
There are other alternative definitions:
Behaviours associated
By definition, aggressive driving is 'committing unprovoked attacks on other drivers', attacks such as not yielding to vehicles wishing to pass.
The U.S. National Highway Traffic Safety Administration (NHTSA) has implemented the Fatality Analysis Reporting System, which identifies actions that would fall under the category of aggressive driving, including:
Following improperly / tailgating.
Improper or erratic lane changing
Illegal driving on a road shoulder, in a ditch, or on a sidewalk or median.
Passing where prohibited.
Operating the vehicle in an erratic, reckless, careless, or negligent manner or suddenly changing speeds without changing lanes.
Failure to yield right of way.
Failure to obey traffic signs, traffic control devices, or traffic officers, failure to observe safety zone traffic laws.
Failure to observe warnings or instructions on vehicle displaying them.
Failure to signal.
Driving too fast for conditions.
Racing.
Making an improper turn.
Close following and sudden braking.
Effects
According to the Fatality Analysis Reporting System, aggressive driving played a role in 56% of fatal crashes between 2003 and 2007, most of which were attributed to excessive speed. Aggressive driving also negatively impacts the environment as it burns 37% more fuel and produces more toxic fumes.
Aggressive driving (abrupt acceleration and frequent slamming on of the brakes) also emits more carbon than a calmer approach. Calm driving would save nearly half a billion tonnes of carbon dioxide by 2050 in China alone.
See also
Bike rage
Brake test
Car chase
Carjacking
Drive-by shooting
Jaywalking
Joyride
Motor vehicle theft
Road rage
Street racing
Tailgating
Traffic stop
Traffic ticket
Legal terms related to aggressive driving:
Reckless driving in United States law
Dangerous driving in United Kingdom law
Driving without due care and attention, legal term in the United States, Ontario in Canada, the United Kingdom, and Ireland
References
External links
National Highway Traffic Safety Administration
Driving
Habits
Road safety | Aggressive driving | [
"Biology"
] | 438 | [
"Behavior",
"Human behavior",
"Habits"
] |
5,719,307 | https://en.wikipedia.org/wiki/Paley%20graph | In mathematics, Paley graphs are undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic tools to be applied to the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally.
Paley graphs are named after Raymond Paley. They are closely related to the Paley construction for constructing Hadamard matrices from quadratic residues.
They were introduced as graphs independently by and . Sachs was interested in them for their self-complementarity properties, while Erdős and Rényi studied their symmetries.
Paley digraphs are directed analogs of Paley graphs that yield antisymmetric conference matrices. They were introduced by (independently of Sachs, Erdős, and Rényi) as a way of constructing tournaments with a property previously known to be held only by random tournaments: in a Paley digraph, every small subset of vertices is dominated by some other vertex.
Definition
Let q be a prime power such that q = 1 (mod 4). That is, q should either be an arbitrary power of a Pythagorean prime (a prime congruent to 1 mod 4) or an even power of an odd non-Pythagorean prime. This choice of q implies that in the unique finite field Fq of order q, the element −1 has a square root.
Now let V = Fq and let
.
If a pair {a,b} is included in E, it is included under either ordering of its two elements. For, a − b = −(b − a), and −1 is a square, from which it follows that a − b is a square if and only if b − a is a square.
By definition G = (V, E) is the Paley graph of order q.
Example
For q = 13, the field Fq is just integer arithmetic modulo 13. The numbers with square roots mod 13 are:
±1 (square roots ±1 for +1, ±5 for −1)
±3 (square roots ±4 for +3, ±6 for −3)
±4 (square roots ±2 for +4, ±3 for −4).
Thus, in the Paley graph, we form a vertex for each of the integers in the range [0,12], and connect each such integer x to six neighbors: x ± 1 (mod 13), x ± 3 (mod 13), and x ± 4 (mod 13).
Properties
The Paley graphs are self-complementary: the complement of any Paley graph is isomorphic to it. One isomorphism is via the mapping that takes a vertex to , where is any nonresidue .
Paley graphs are strongly regular graphs, with parameters
This in fact follows from the fact that the graph is arc-transitive and self-complementary. The strongly regular graphs with parameters of this form (for an arbitrary ) are called conference graphs, so the Paley graphs form an infinite family of conference graphs. The adjacency matrix of a conference graph, such as a Paley graph, can be used to construct a conference matrix, and vice versa. These are matrices whose coefficients are , with zero on the diagaonal, that give a scalar multiple of the identity matrix when multiplied by their transpose.
The eigenvalues of Paley graphs are (with multiplicity 1) and (both with multiplicity ). They can be calculated using the quadratic Gauss sum or by using the theory of strongly regular graphs.
If is prime, the isoperimetric number of the Paley graph satisfies the following bounds:
When is prime, the associated Paley graph is a Hamiltonian circulant graph.
Paley graphs are quasi-random: the number of times each possible constant-order graph occurs as a subgraph of a Paley graph is (in the limit for large ) the same as for random graphs, and large sets of vertices have approximately the same number of edges as they would in random graphs.
The Paley graph of order 9 is a locally linear graph, a rook's graph, and the graph of the 3-3 duoprism.
The Paley graph of order 13 has book thickness 4 and queue number 3.
The Paley graph of order 17 is the unique largest graph G such that neither G nor its complement contains a complete 4-vertex subgraph. It follows that the Ramsey number R(4, 4) = 18.
The Paley graph of order 101 is currently the largest known graph G such that neither G nor its complement contains a complete 6-vertex subgraph.
Sasukara et al. (1993) use Paley graphs to generalize the construction of the Horrocks–Mumford bundle.
Paley digraphs
Let q be a prime power such that q = 3 (mod 4). Thus, the finite field of order q, Fq, has no square root of −1. Consequently, for each pair (a,b) of distinct elements of Fq, either a − b or b − a, but not both, is a square. The Paley digraph is the directed graph with vertex set V = Fq and arc set
The Paley digraph is a tournament because each pair of distinct vertices is linked by an arc in one and only one direction.
The Paley digraph leads to the construction of some antisymmetric conference matrices and biplane geometries.
Genus
The six neighbors of each vertex in the Paley graph of order 13 are connected in a cycle; that is, the graph is locally cyclic. Therefore, this graph can be embedded as a Whitney triangulation of a torus, in which every face is a triangle and every triangle is a face. More generally, if any Paley graph of order q could be embedded so that all its faces are triangles, we could calculate the genus of the resulting surface via the Euler characteristic as . Bojan Mohar conjectures that the minimum genus of a surface into which a Paley graph can be embedded is near this bound in the case that q is a square, and questions whether such a bound might hold more generally. Specifically, Mohar conjectures that the Paley graphs of square order can be embedded into surfaces with genus
where the o(1) term can be any function of q that goes to zero in the limit as q goes to infinity.
finds embeddings of the Paley graphs of order q ≡ 1 (mod 8) that are highly symmetric and self-dual, generalizing a natural embedding of the Paley graph of order 9 as a 3×3 square grid on a torus. However the genus of White's embeddings is higher by approximately a factor of three than Mohar's conjectured bound.
References
Further reading
External links
Number theory
Parametric families of graphs
Regular graphs
Strongly regular graphs | Paley graph | [
"Mathematics"
] | 1,457 | [
"Discrete mathematics",
"Number theory"
] |
5,719,641 | https://en.wikipedia.org/wiki/Rajiv%20Gupta%20%28technocrat%29 | Rajiv Gupta is an engineer, a repeat entrepreneur and currently an executive at McAfee.
Early life
Gupta earned a bachelor's degree from the Indian Institute of Technology Kharagpur around 1984. He received his Ph.D. in compiler optimization from the California Institute of Technology (Caltech) in 1990. He married a British woman, Debra and they have two children - Veda and Anya. He resides in Los Altos.
Career
Gupta joined Hewlett-Packard in 1990, and developed the IA-64 architecture, which HP called WideWord and Intel marketed as Itanium.
From 1995 he developed a client utility project at HP Labs, which was an early example of a service-oriented architecture for Web services.
He was co-creator and general manager of the E-speak project when it was announced in 1999.
Around the same time, he supported his brother Sanjiv Gupta, to start Bodhtree Consulting, Ltd., in Hyderabad, India.
The E-speak technology was abandoned in late 2001.
In 2002, Gupta founded Confluent Software, developing what became the CoreSV product. It was acquired by Oblix in February 2004, which in turn was acquired by Oracle Corporation in March, 2005.
In 2005 he founded Securent, which was acquired by Cisco in November 2007 for an estimated $100 million.
He has more than 45 patents.
In 2011 Gupta founded Skyhigh Networks. The first round of financing was led by Greylock Partners in April, 2012, for about $6.5 million.
The company raised $20 million in May, 2013, led by Sequoia Capital.
Another investment of $40 million was announced in June, 2014, from existing investors and Salesforce.com.
On November 28, 2017, McAfee announced it would acquire Skyhigh Networks and appoint Rajiv Gupta as the head of McAfee's entire cloud business.
References
People in information technology
California Institute of Technology alumni
Living people
IIT Kharagpur alumni
Hewlett-Packard people
1963 births | Rajiv Gupta (technocrat) | [
"Technology"
] | 416 | [
"People in information technology",
"Information technology"
] |
5,719,764 | https://en.wikipedia.org/wiki/Phenylhydrazine | Phenylhydrazine is the chemical compound with the formula . It is often abbreviated as . It is also found in edible mushrooms.
Properties
Phenylhydrazine forms monoclinic prisms that melt to an oil around room temperature which may turn yellow to dark red upon exposure to air. Phenylhydrazine is miscible with ethanol, diethyl ether, chloroform and benzene. It is sparingly soluble in water.
Preparation
Phenylhydrazine is prepared by reacting aniline with sodium nitrite in the presence of hydrogen chloride to form the diazonium salt, which is subsequently reduced using sodium sulfite in the presence of sodium hydroxide to form the final product.
History
Phenylhydrazine was the first hydrazine derivative characterized, reported by Hermann Emil Fischer in 1875. He prepared it by reduction of a phenyl diazonium salt using sulfite salts. Fischer used phenylhydrazine to characterize sugars via formation of hydrazones known as osazones with the sugar aldehyde. He also demonstrated in this first paper many of the key properties recognized for hydrazines.
Uses
Phenylhydrazine is used to prepare indoles by the Fischer indole synthesis, which are intermediates in the synthesis of various dyes and pharmaceuticals.
Phenylhydrazine is used to form phenylhydrazones of natural mixtures of simple sugars in order to render the differing sugars easily separable from each other.
This molecule is also used to induce acute hemolytic anemia in animal models.
Safety
Exposure to phenylhydrazine may cause contact dermatitis, hemolytic anemia, and liver damage.
References
External links
PubChem
Additional chemical properties of phenylhydrazine
CDC - NIOSH Pocket Guide to Chemical Hazards
Hydrazines
Monoamine oxidase inhibitors
Emil Fischer
Phenyl compounds | Phenylhydrazine | [
"Chemistry"
] | 403 | [
"Functional groups",
"Hydrazines"
] |
5,719,783 | https://en.wikipedia.org/wiki/Multiple%20edges | In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or in a directed graph, two or more edges with both the same tail vertex and the same head vertex. A simple graph has no multiple edges and no loops.
Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops):
Where graphs are defined so as to allow multiple edges and loops, a graph without loops or multiple edges is often distinguished from other graphs by calling it a simple graph.
Where graphs are defined so as to disallow multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which can have multiple edges.
Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view. Additionally, they constitute the core differentiating feature of multidimensional networks.
A planar graph remains planar if an edge is added between two vertices already joined by an edge; thus, adding multiple edges preserves planarity.
A dipole graph is a graph with two vertices, in which all edges are parallel to each other.
Notes
References
Balakrishnan, V. K.; Graph Theory, McGraw-Hill; 1 edition (February 1, 1997). .
Bollobás, Béla; Modern Graph Theory, Springer; 1st edition (August 12, 2002). .
Diestel, Reinhard; Graph Theory, Springer; 2nd edition (February 18, 2000). .
Gross, Jonathon L, and Yellen, Jay; Graph Theory and Its Applications, CRC Press (December 30, 1998). .
Gross, Jonathon L, and Yellen, Jay; (eds); Handbook of Graph Theory. CRC (December 29, 2003). .
Zwillinger, Daniel; CRC Standard Mathematical Tables and Formulae, Chapman & Hall/CRC; 31st edition (November 27, 2002). .
Graph theory objects | Multiple edges | [
"Mathematics"
] | 442 | [
"Mathematical relations",
"Graph theory objects",
"Graph theory"
] |
5,719,915 | https://en.wikipedia.org/wiki/Babulang | Babulang is the largest festival of the traditional Bisaya community of Limbang, Sarawak. The festival showcases various music, songs, dances, colourful traditional costumes, decorations and handicrafts.
The festival includes a Ratu Babulang competition, and Water buffalo races.
References
Cultural conventions
Ritual | Babulang | [
"Biology"
] | 60 | [
"Behavior",
"Human behavior",
"Ritual"
] |
5,719,961 | https://en.wikipedia.org/wiki/Benzhydryl%20compounds | The benzhydryl compounds are a group of organic compounds whose parent structures include diphenylmethane (which is two benzene rings connected by a single methane), with any number of attached substituents, including bridges. This group typically excludes compounds in which either benzene is fused to another ring (bicyclic, tricyclic, polycyclic) or includes a heteroatom, or where the methane connects to three or four benzenes.
The benzhydryl radical can be abbreviated or Bzh.
Carboaromatic
Alcohols
Acyclic: pridinol
Pyrolidino: diphenylprolinol
2-Piperidine: pipradrol
4-Piperidine: terfenadine, fexofenadine
Benzilic ester: QNB, JB-336, JB-318, benactyzine
Alkenes
Tricycle: amitriptyline, melitracen, cyclobenzaprine, tianeptine, amineptine, clopenthixol, chlorprothixene, flupentixol, thiothixene, zuclopenthixol
Tricyclic and piperidine: pimethixene, cyproheptadine
Acyclic: gilutensin
Alkyl(amine)s
Acyclic: (3-phenylpropylamine), tolpropamine, tolterodine
Piperidine: desoxypipradrol, budipine
N-alkyl-4-piperidinol: penfluridol
N-arylalkyl-piperidine: pimozide
Tetrahydronaphthalene: tametraline (4-phenylaminotetralin), sertraline
Tetrahydroisoquinoline: nomifensine, diclofensine "tetrahydronaphisoquinoline", dinapsoline (see doxanthrine and dinoxyline)
Pyrroloisoquinoline: JNJ-7925476
Indanamine: Lu 19-005
Tricyclic: 9-Aminomethyl-9,10-dihydroanthracene, phenindamine (see MPTP)
Tetracyclic: maprotiline, dihydrexidine, butaclamol, ecopipam
Tetrahydrobenzazepine: SKF-83959, SKF-82958, SKF-81297, SKF 38393, fenoldopam, 6-Br-APB, SCH 23390
Piperazine: amperozide
Triazaspiro: fluspirilene
Alkoxy compounds
Acyclic (3 °C): diphenhydramine (c.f deramciclane), orphenadrine, p-methyldiphenhydramine
Acyclic (4 °C): moxastine, Clemastine, embramine,
Piperazine: GBR-12935, GBR 12909, DBL-583
Tropine: benztropine, deptropine, etybenzatropine, difluoropine
Piperidine: diphenylpyraline
Phthalane: talopram, citalopram
Octahedral: nefopam
Benzdihydropyran: A-68930 (isochromene)
Amines
Piperazine: cyclizine, clocinizine, hydroxyzine, meclozine, cetirizine, dotarizine, cinnarizine
Benzazepine: mianserin
Tetracyclic: dizocilpine
Other
Aromatic alkoxy: bifemelane, phenyltoloxamine
Keto: phenadoxone, methadone, dipipanone, etc.
Amido: dextromoramide
Imino: benzodiazepine, GYKI-52895
Sulfinyl: modafinil, adrafinil
Pituxate gem-diphenylcyclopropane
Heteroaromatic
These species are not strictly benzhydryl-containing but are analogous.
Heteroaromatic rings
Alkene: thiambutene, loratadine
Alkylamine: A-86929, amfonelic acid
Benzenes linked by a non-carbon atom
Nitrogen: promethazine, imipramine, acepromazine, chlorpromazine, fluphenazine, mesoridazine, levomepromazine, perazine, periciazine, perphenazine, prochlorperazine, sulforidazine, thioridazine, trifluoperazine, triflupromazine, clozapine, thiethylperazine
Indolic nitrogen: sertindole
Oxygen: loxapine, asenapine, tyrima
Benzene and heterocycle linked through a non-carbon
Olanzapine
References
External links
, a.k.a. called benzhydryl bromide
, not called benzhydryl bromide
Aromatic compounds | Benzhydryl compounds | [
"Chemistry"
] | 1,113 | [
"Organic compounds",
"Aromatic compounds"
] |
5,720,090 | https://en.wikipedia.org/wiki/Benzylidene%20compounds | Benzylidene compounds are, formally speaking, derivatives of benzylidene, although few are prepared from the carbene. Benzylidene acetal is a protecting group in synthetic organic chemistry of the form PhCH(OR)2. For example, 4,6-O-benzylidene-glucopyranose is a glucose derivative. Benzylidene is an archaic term for compounds of the type PhCHX2 and PhCH= substituents (Ph = C6H5). For example, dibenzylideneacetone is (PhCH=CH)2CO. Benzal chloride, PhCHCl2, is alternatively named benzylidene chloride.
Benzylidene is the molecule C6H5CH. It is a triplet carbene (CAS RN 3101-08-4). It is generated by irradiation of phenyldiazomethane.
See also
Aurone
3,5-Difluoro-4-hydroxybenzylidene imidazolinone
References
External links
Aromatic compounds | Benzylidene compounds | [
"Chemistry"
] | 229 | [
"Organic compounds",
"Aromatic compounds"
] |
361,449 | https://en.wikipedia.org/wiki/Descent%20%28mathematics%29 | In mathematics, the idea of descent extends the intuitive idea of 'gluing' in topology. Since the topologists' glue is the use of equivalence relations on topological spaces, the theory starts with some ideas on identification.
Descent of vector bundles
The case of the construction of vector bundles from data on a disjoint union of topological spaces is a straightforward place to start.
Suppose X is a topological space covered by open sets Xi. Let Y be the disjoint union of the Xi, so that there is a natural mapping
We think of Y as 'above' X, with the Xi projection 'down' onto X. With this language, descent implies a vector bundle on Y (so, a bundle given on each Xi), and our concern is to 'glue' those bundles Vi, to make a single bundle V on X. What we mean is that V should, when restricted to Xi, give back Vi, up to a bundle isomorphism.
The data needed is then this: on each overlap
intersection of Xi and Xj, we'll require mappings
to use to identify Vi and Vj there, fiber by fiber. Further the fij must satisfy conditions based on the reflexive, symmetric and transitive properties of an equivalence relation (gluing conditions). For example, the composition
for transitivity (and choosing apt notation). The fii should be identity maps and hence symmetry becomes (so that it is fiberwise an isomorphism).
These are indeed standard conditions in fiber bundle theory (see transition map). One important application to note is change of fiber: if the fij are all you need to make a bundle, then there are many ways to make an associated bundle. That is, we can take essentially same fij, acting on various fibers.
Another major point is the relation with the chain rule: the discussion of the way there of constructing tensor fields can be summed up as 'once you learn to descend the tangent bundle, for which transitivity is the Jacobian chain rule, the rest is just 'naturality of tensor constructions'.
To move closer towards the abstract theory we need to interpret the disjoint union of the
now as
the fiber product (here an equalizer) of two copies of the projection p. The bundles on the Xij that we must control are V′ and V", the pullbacks to the fiber of V via the two different projection maps to X.
Therefore, by going to a more abstract level one can eliminate the combinatorial side (that is, leave out the indices) and get something that makes sense for p not of the special form of covering with which we began. This then allows a category theory approach: what remains to do is to re-express the gluing conditions.
History
The ideas were developed in the period 1955–1965 (which was roughly the time at which the requirements of algebraic topology were met but those of algebraic geometry were not). From the point of view of abstract category theory the work of comonads of Beck was a summation of those ideas; see Beck's monadicity theorem.
The difficulties of algebraic geometry with passage to the quotient are acute. The urgency (to put it that way) of the problem for the geometers accounts for the title of the 1959 Grothendieck seminar TDTE on theorems of descent and techniques of existence (see FGA) connecting the descent question with the representable functor question in algebraic geometry in general, and the moduli problem in particular.
Fully faithful descent
Let . Each sheaf F on X gives rise to a descent datum
,
where satisfies the cocycle condition
.
The fully faithful descent says: The functor is fully faithful. Descent theory tells conditions for which there is a fully faithful descent, and when this functor is an equivalence of categories.
See also
Grothendieck connection
Stack (mathematics)
Galois descent
Grothendieck topology
Fibered category
Beck's monadicity theorem
Cohomological descent
References
SGA 1, Ch VIII – this is the main reference
A chapter on the descent theory is more accessible than SGA.
Further reading
Other possible sources include:
Angelo Vistoli, Notes on Grothendieck topologies, fibered categories and descent theory
Mattieu Romagny, A straight way to algebraic stacks
External links
What is descent theory?
Topology
Category theory
Algebraic geometry | Descent (mathematics) | [
"Physics",
"Mathematics"
] | 899 | [
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"Mathematical structures",
"Algebraic geometry",
"Mathematical objects",
"Fields of abstract algebra",
"Topology",
"Space",
"Category theory",
"Mathematical relations",
"Geometry",
"Spacetime"
] |
361,558 | https://en.wikipedia.org/wiki/Strangling | Strangling or strangulation is compression of the neck that may lead to unconsciousness or death by causing an increasingly hypoxic state in the brain by restricting the flow of oxygen through the trachea. Fatal strangulation typically occurs in cases of violence, accidents, and is one of two main ways that hanging causes death (alongside breaking the victim's neck).
Strangling does not have to be fatal; limited or interrupted strangling is practised in erotic asphyxia, in the choking game, and is an important technique in many combat sports and self-defense systems. Strangling can be divided into three general types according to the mechanism used:
Hanging — Suspension from a cord wound around the neck
Ligature strangulation — Strangulation without suspension using some form of cord-like object (ligature) called a garrote
Manual strangulation — Strangulation using the fingers (hands) or other extremity
General
Strangling involves one or several mechanisms that interfere with the normal flow of oxygen into the brain:
Compression of the carotid arteries or jugular veins—causing cerebral ischemia.
Compression of the laryngopharynx, larynx, or trachea—causing asphyxia.
Stimulation of the carotid sinus reflex—causing bradycardia, hypotension, or both.
Depending on the particular method of strangulation, one or several of these typically occur in combination; vascular obstruction is usually the main mechanism. Complete obstruction of blood flow to the brain is associated with irreversible neurological damage and death, but during strangulation there is still unimpeded blood flow in the vertebral arteries. Estimates have been made that significant occlusion of the carotid arteries and jugular veins occurs with a pressure of around , while the trachea demands six times more at approximately .
As in all cases of strangulation, the rapidity of death can be affected by the susceptibility to carotid sinus stimulation. Carotid sinus reflex death is sometimes considered a mechanism of death in cases of strangulation, but it remains highly disputed. The reported time from application to unconsciousness varies from 7–14 seconds if effectively applied to one minute in other cases, with death occurring minutes after unconsciousness.
Manual strangulation
Manual strangulation (also known as "throttling") is strangling with the hands, fingers, or other extremities and sometimes also with blunt objects, such as batons. Depending on how the strangling is performed, it may compress the airway, interfere with the flow of blood in the neck, or work as a combination of the two. Consequently, manual strangulation may damage the larynx and fracture the hyoid or other bones in the neck. In cases of airway compression, manual strangling leads to the frightening sensation of air hunger and may induce violent struggling.
Manual strangulation is common in situations of domestic violence, and is regarded by experts as an especially severe form of domestic violence, due to its extremely frightening and potentially lethal nature, and an observed correlation between non-fatal strangulation in domestic violence and future homicide.
Manual strangulation also has a history as a form of capital punishment, during the 18th century, a sentence of "Death by Throttling" would be passed upon the verdict of a court martial for the crime of desertion from the British Army.
More technical variants of manual strangulation are referred to as strangleholds, or chokeholds (despite the term "choke" more technically referring to internal airway restriction), and are extensively practised and used in various martial arts, combat sports, self-defense systems, and in military hand-to-hand combat application. In some martial arts like judo, Brazilian jiu-jitsu, and jujutsu, when applied correctly and released promptly after loss of consciousness, strangleholds that constrict blood flow are regarded as a safer means to render an opponent unconscious, when compared to other methods, especially strikes to the head, the latter of which can cause potentially catastrophic or fatal and irreversible brain injuries much more quickly and unpredictably.
Ligature strangulation
Ligature strangulation or garroting is strangling with some form of cord such as rope, wire, chain, or shoelaces (a garrote) either partially or fully circumferencing the neck. Even though the mechanism of strangulation is similar, it is usually distinguished from hanging by the strangling force being something other than the person's own body weight. Incomplete occlusion of the carotid arteries is expected and, in cases of homicide, the victim may struggle for a period of time, with unconsciousness typically occurring in 10 to 15 seconds. Cases of ligature strangulation generally involve homicides of women, children, and the elderly. Compared to hanging, the ligature mark will most likely be located lower on the neck of the victim.
During the Spanish Inquisition, victims who admitted their alleged sins and recanted were killed via ligature strangulation (i.e. the garrote) before their bodies were burnt during the auto-da-fé. Throughout much of the 20th and 21st centuries, the American Mafia used ligature strangulation as a means of murdering their victims. Confessed American serial killer Altemio Sanchez used ligature strangulation in the rapes and/or murders of his victims, as did Gary Ridgway (the Green River Killer) and British serial killer Dennis Nilsen.
Incaprettamento is a method of strangulation in which the victims neck is tied to their legs bent behind their back (similar to hogtie), so that the victim effectively strangle themselves. This method was common throughout Neolithic Europe, and occurred for over two thousands years in northern and southern Europe, as evidenced by skeleton remains. It is uncertain why it was so common, but researchers speculate a person bound in this way might be considered to have strangled themselves, versus being killed by someone else. Victims may have been part of a ritual sacrifice. Rock art in Addaura Cave, in Sicily, made between 16,000 and 13,000 BP, depict two human figures bound in the incaprettamento manner. Today, it is a method of homicide mostly associated with the Italian Mafia, who have used it as a ritual warning or reprimand.
See also
Beheading
Capital punishment
Fainting game
Hanging
Long drop
Short drop
Strangulation in domestic violence
Thuggee
References
Sources
Basic reference on judo choking techniques.
Abuse
Violence
Execution methods
Causes of death | Strangling | [
"Biology"
] | 1,381 | [
"Behavior",
"Abuse",
"Violence",
"Aggression",
"Human behavior"
] |
361,598 | https://en.wikipedia.org/wiki/Second%20Hardy%E2%80%93Littlewood%20conjecture | In number theory, the second Hardy–Littlewood conjecture concerns the number of primes in intervals. Along with the first Hardy–Littlewood conjecture, the second Hardy–Littlewood conjecture was proposed by G. H. Hardy and John Edensor Littlewood in 1923.
Statement
The conjecture states that
for integers , where denotes the prime-counting function, giving the number of prime numbers up to and including .
Connection to the first Hardy–Littlewood conjecture
The statement of the second Hardy–Littlewood conjecture is equivalent to the statement that the number of primes from to is always less than or equal to the number of primes from 1 to . This was proved to be inconsistent with the first Hardy–Littlewood conjecture on prime -tuples, and the first violation is expected to likely occur for very large values of . For example, an admissible k-tuple (or prime constellation) of 447 primes can be found in an interval of integers, while . If the first Hardy–Littlewood conjecture holds, then the first such -tuple is expected for greater than but less than .
References
External links
Analytic number theory
Conjectures about prime numbers
Unsolved problems in number theory | Second Hardy–Littlewood conjecture | [
"Mathematics"
] | 241 | [
"Unsolved problems in mathematics",
"Analytic number theory",
"Number theory stubs",
"Unsolved problems in number theory",
"Mathematical problems",
"Number theory"
] |
361,609 | https://en.wikipedia.org/wiki/Moduli%20space | In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Bernhard Riemann first used the term "moduli" in 1857.
Motivation
Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they are isomorphic (that is, geometrically the same). Moduli spaces can be thought of as giving a universal space of parameters for the problem. For example, consider the problem of finding all circles in the Euclidean plane up to congruence. Any circle can be described uniquely by giving three points, but many different sets of three points give the same circle: the correspondence is many-to-one. However, circles are uniquely parameterized by giving their center and radius: this is two real parameters and one positive real parameter. Since we are only interested in circles "up to congruence", we identify circles having different centers but the same radius, and so the radius alone suffices to parameterize the set of interest. The moduli space is, therefore, the positive real numbers.
Moduli spaces often carry natural geometric and topological structures as well. In the example of circles, for instance, the moduli space is not just an abstract set, but the absolute value of the difference of the radii defines a metric for determining when two circles are "close". The geometric structure of moduli spaces locally tells us when two solutions of a geometric classification problem are "close", but generally moduli spaces also have a complicated global structure as well.
For example, consider how to describe the collection of lines in R2 that intersect the origin. We want to assign to each line L of this family a quantity that can uniquely identify it—a modulus. An example of such a quantity is the positive angle θ(L) with 0 ≤ θ < π radians. The set of lines L so parametrized is known as P1(R) and is called the real projective line.
We can also describe the collection of lines in R2 that intersect the origin by means of a topological construction. To wit: consider the unit circle S1 ⊂ R2 and notice that every point s ∈ S1 gives a line L(s) in the collection (which joins the origin and s). However, this map is two-to-one, so we want to identify s ~ −s to yield P1(R) ≅ S1/~ where the topology on this space is the quotient topology induced by the quotient map S1 → P1(R).
Thus, when we consider P1(R) as a moduli space of lines that intersect the origin in R2, we capture the ways in which the members (lines in this case) of the family can modulate by continuously varying 0 ≤ θ < π.
Basic examples
Projective space and Grassmannians
The real projective space Pn is a moduli space that parametrizes the space of lines in Rn+1 which pass through the origin. Similarly, complex projective space is the space of all complex lines in Cn+1 passing through the origin.
More generally, the Grassmannian G(k, V) of a vector space V over a field F is the moduli space of all k-dimensional linear subspaces of V.
Projective space as moduli of very ample line bundles generated by global sections
Whenever there is an embedding of a scheme into the universal projective space , the embedding is given by a line bundle and sections which all don't vanish at the same time. This means, given a pointthere is an associated pointgiven by the compositionsThen, two line bundles with sections are equivalentiff there is an isomorphism such that . This means the associated moduli functor sends a scheme to the setShowing this is true can be done by running through a series of tautologies: any projective embedding gives the globally generated sheaf with sections . Conversely, given an ample line bundle globally generated by sections gives an embedding as above.
Chow variety
The Chow variety Chow(d,P3) is a projective algebraic variety which parametrizes degree d curves in P3. It is constructed as follows. Let C be a curve of degree d in P3, then consider all the lines in P3 that intersect the curve C. This is a degree d divisor DC in G(2, 4), the Grassmannian of lines in P3. When C varies, by associating C to DC, we obtain a parameter space of degree d curves as a subset of the space of degree d divisors of the Grassmannian: Chow(d,P3).
Hilbert scheme
The Hilbert scheme Hilb(X) is a moduli scheme. Every closed point of Hilb(X) corresponds to a closed subscheme of a fixed scheme X, and every closed subscheme is represented by such a point. A simple example of a Hilbert scheme is the Hilbert scheme parameterizing degree hypersurfaces of projective space . This is given by the projective bundlewith universal family given bywhere is the associated projective scheme for the degree homogeneous polynomial .
Definitions
There are several related notions of things we could call moduli spaces. Each of these definitions formalizes a different notion of what it means for the points of space M to represent geometric objects.
Fine moduli spaces
This is the standard concept. Heuristically, if we have a space M for which each point m ∊ M corresponds to an algebro-geometric object Um, then we can assemble these objects into a tautological family U over M. (For example, the Grassmannian G(k, V) carries a rank k bundle whose fiber at any point [L] ∊ G(k, V) is simply the linear subspace L ⊂ V.) M is called a base space of the family U. We say that such a family is universal if any family of algebro-geometric objects T over any base space B is the pullback of U along a unique map B → M. A fine moduli space is a space M which is the base of a universal family.
More precisely, suppose that we have a functor F from schemes to sets, which assigns to a scheme B the set of all suitable families of objects with base B. A space M is a fine moduli space for the functor F if M represents F, i.e., there is a natural isomorphism
τ : F → Hom(−, M), where Hom(−, M) is the functor of points. This implies that M carries a universal family; this family is the family on M corresponding to the identity map 1M ∊ Hom(M, M).
Coarse moduli spaces
Fine moduli spaces are desirable, but they do not always exist and are frequently difficult to construct, so mathematicians sometimes use a weaker notion, the idea of a coarse moduli space. A space M is a coarse moduli space for the functor F if there exists a natural transformation τ : F → Hom(−, M) and τ is universal among such natural transformations. More concretely, M is a coarse moduli space for F if any family T over a base B gives rise to a map φT : B → M and any two objects V and W (regarded as families over a point) correspond to the same point of M if and only if V and W are isomorphic. Thus, M is a space which has a point for every object that could appear in a family, and whose geometry reflects the ways objects can vary in families. Note, however, that a coarse moduli space does not necessarily carry any family of appropriate objects, let alone a universal one.
In other words, a fine moduli space includes both a base space M and universal family U → M, while a coarse moduli space only has the base space M.
Moduli stacks
It is frequently the case that interesting geometric objects come equipped with many natural automorphisms. This in particular makes the existence of a fine moduli space impossible (intuitively, the idea is that if L is some geometric object, the trivial family L × [0,1] can be made into a twisted family on the circle S1 by identifying L × {0} with L × {1} via a nontrivial automorphism. Now if a fine moduli space X existed, the map S1 → X should not be constant, but would have to be constant on any proper open set by triviality), one can still sometimes obtain a coarse moduli space. However, this approach is not ideal, as such spaces are not guaranteed to exist, they are frequently singular when they do exist, and miss details about some non-trivial families of objects they classify.
A more sophisticated approach is to enrich the classification by remembering the isomorphisms. More precisely, on any base B one can consider the category of families on B with only isomorphisms between families taken as morphisms. One then considers the fibred category which assigns to any space B the groupoid of families over B. The use of these categories fibred in groupoids to describe a moduli problem goes back to Grothendieck (1960/61). In general, they cannot be represented by schemes or even algebraic spaces, but in many cases, they have a natural structure of an algebraic stack.
Algebraic stacks and their use to analyze moduli problems appeared in Deligne-Mumford (1969) as a tool to prove the irreducibility of the (coarse) moduli space of curves of a given genus. The language of algebraic stacks essentially provides a systematic way to view the fibred category that constitutes the moduli problem as a "space", and the moduli stack of many moduli problems is better-behaved (such as smooth) than the corresponding coarse moduli space.
Further examples
Moduli of curves
The moduli stack classifies families of smooth projective curves of genus g, together with their isomorphisms. When g > 1, this stack may be compactified by adding new "boundary" points which correspond to stable nodal curves (together with their isomorphisms). A curve is stable if it has only a finite group of automorphisms. The resulting stack is denoted . Both moduli stacks carry universal families of curves. One can also define coarse moduli spaces representing isomorphism classes of smooth or stable curves. These coarse moduli spaces were actually studied before the notion of moduli stack was invented. In fact, the idea of a moduli stack was invented by Deligne and Mumford in an attempt to prove the projectivity of the coarse moduli spaces. In recent years, it has become apparent that the stack of curves is actually the more fundamental object.
Both stacks above have dimension 3g−3; hence a stable nodal curve can be completely specified by choosing the values of 3g−3 parameters, when g > 1. In lower genus, one must account for the presence of smooth families of automorphisms, by subtracting their number. There is exactly one complex curve of genus zero, the Riemann sphere, and its group of isomorphisms is PGL(2). Hence, the dimension of is
dim(space of genus zero curves) − dim(group of automorphisms) = 0 − dim(PGL(2)) = −3.
Likewise, in genus 1, there is a one-dimensional space of curves, but every such curve has a one-dimensional group of automorphisms. Hence, the stack has dimension 0. The coarse moduli spaces have dimension 3g−3 as the stacks when g > 1 because the curves with genus g > 1 have only a finite group as its automorphism i.e. dim(a group of automorphisms) = 0. Eventually, in genus zero, the coarse moduli space has dimension zero, and in genus one, it has dimension one.
One can also enrich the problem by considering the moduli stack of genus g nodal curves with n marked points. Such marked curves are said to be stable if the subgroup of curve automorphisms which fix the marked points is finite. The resulting moduli stacks of smooth (or stable) genus g curves with n-marked points are denoted (or ), and have dimension 3g − 3 + n.
A case of particular interest is the moduli stack of genus 1 curves with one marked point. This is the stack of elliptic curves, and is the natural home of the much studied modular forms, which are meromorphic sections of bundles on this stack.
Moduli of varieties
In higher dimensions, moduli of algebraic varieties are more difficult to construct and study. For instance, the higher-dimensional analogue of the moduli space of elliptic curves discussed above is the moduli space of abelian varieties, such as the Siegel modular variety. This is the problem underlying Siegel modular form theory. See also Shimura variety.
Using techniques arising out of the minimal model program, moduli spaces of varieties of general type were constructed by János Kollár and Nicholas Shepherd-Barron, now known as KSB moduli spaces.
Using techniques arising out of differential geometry and birational geometry simultaneously, the construction of moduli spaces of Fano varieties has been achieved by restricting to a special class of K-stable varieties. In this setting important results about boundedness of Fano varieties proven by Caucher Birkar are used, for which he was awarded the 2018 Fields medal.
The construction of moduli spaces of Calabi-Yau varieties is an important open problem, and only special cases such as moduli spaces of K3 surfaces or Abelian varieties are understood.
Moduli of vector bundles
Another important moduli problem is to understand the geometry of (various substacks of) the moduli stack Vectn(X) of rank n vector bundles on a fixed algebraic variety X. This stack has been most studied when X is one-dimensional, and especially when n equals one. In this case, the coarse moduli space is the Picard scheme, which like the moduli space of curves, was studied before stacks were invented. When the bundles have rank 1 and degree zero, the study of coarse moduli space is the study of the Jacobian variety.
In applications to physics, the number of moduli of vector bundles and the closely related problem of the number of moduli of principal G-bundles has been found to be significant in gauge theory.
Volume of the moduli space
Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces.
Methods for constructing moduli spaces
The modern formulation of moduli problems and definition of moduli spaces in terms of the moduli functors (or more generally the categories fibred in groupoids), and spaces (almost) representing them, dates back to Grothendieck (1960/61), in which he described the general framework, approaches, and main problems using Teichmüller spaces in complex analytical geometry as an example. The talks, in particular, describe the general method of constructing moduli spaces by first rigidifying the moduli problem under consideration.
More precisely, the existence of non-trivial automorphisms of the objects being classified makes it impossible to have a fine moduli space. However, it is often possible to consider a modified moduli problem of classifying the original objects together with additional data, chosen in such a way that the identity is the only automorphism respecting also the additional data. With a suitable choice of the rigidifying data, the modified moduli problem will have a (fine) moduli space T, often described as a subscheme of a suitable Hilbert scheme or Quot scheme. The rigidifying data is moreover chosen so that it corresponds to a principal bundle with an algebraic structure group G. Thus one can move back from the rigidified problem to the original by taking quotient by the action of G, and the problem of constructing the moduli space becomes that of finding a scheme (or more general space) that is (in a suitably strong sense) the quotient T/G of T by the action of G. The last problem, in general, does not admit a solution; however, it is addressed by the groundbreaking geometric invariant theory (GIT), developed by David Mumford in 1965, which shows that under suitable conditions the quotient indeed exists.
To see how this might work, consider the problem of parametrizing smooth curves of the genus g > 2. A smooth curve together with a complete linear system of degree d > 2g is equivalent to a closed one dimensional subscheme of the projective space Pd−g. Consequently, the moduli space of smooth curves and linear systems (satisfying certain criteria) may be embedded in the Hilbert scheme of a sufficiently high-dimensional projective space. This locus H in the Hilbert scheme has an action of PGL(n) which mixes the elements of the linear system; consequently, the moduli space of smooth curves is then recovered as the quotient of H by the projective general linear group.
Another general approach is primarily associated with Michael Artin. Here the idea is to start with an object of the kind to be classified and study its deformation theory. This means first constructing infinitesimal deformations, then appealing to prorepresentability theorems to put these together into an object over a formal base. Next, an appeal to Grothendieck's formal existence theorem provides an object of the desired kind over a base which is a complete local ring. This object can be approximated via Artin's approximation theorem by an object defined over a finitely generated ring. The spectrum of this latter ring can then be viewed as giving a kind of coordinate chart on the desired moduli space. By gluing together enough of these charts, we can cover the space, but the map from our union of spectra to the moduli space will, in general, be many to one. We, therefore, define an equivalence relation on the former; essentially, two points are equivalent if the objects over each are isomorphic. This gives a scheme and an equivalence relation, which is enough to define an algebraic space (actually an algebraic stack if we are being careful) if not always a scheme.
In physics
The term moduli space is sometimes used in physics to refer specifically to the moduli space of vacuum expectation values of a set of scalar fields, or to the moduli space of possible string backgrounds.
Moduli spaces also appear in physics in topological field theory, where one can use Feynman path integrals to compute the intersection numbers of various algebraic moduli spaces.
See also
Construction tools
Hilbert scheme
Quot scheme
Deformation theory
GIT quotient
Artin's criterion, general criterion for constructing moduli spaces as algebraic stacks from moduli functors
Moduli spaces
Moduli of algebraic curves
Moduli stack of elliptic curves
Moduli spaces of K-stable Fano varieties
Modular curve
Picard functor
Moduli of semistable sheaves on a curve
Kontsevich moduli space
Moduli of semistable sheaves
References
Notes
Moduli theory
Moduli stacks in P-adic modular forms and Langlands program
Research articles
Fundamental papers
Mumford, David, Geometric invariant theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Band 34 Springer-Verlag, Berlin-New York 1965 vi+145 pp
Mumford, David; Fogarty, J.; Kirwan, F. Geometric invariant theory. Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) (Results in Mathematics and Related Areas (2)), 34. Springer-Verlag, Berlin, 1994. xiv+292 pp.
Early applications
Other references
Papadopoulos, Athanase, ed. (2007), Handbook of Teichmüller theory. Vol. I, IRMA Lectures in Mathematics and Theoretical Physics, 11, European Mathematical Society (EMS), Zürich, , ,
Papadopoulos, Athanase, ed. (2009), Handbook of Teichmüller theory. Vol. II, IRMA Lectures in Mathematics and Theoretical Physics, 13, European Mathematical Society (EMS), Zürich, , ,
Papadopoulos, Athanase, ed. (2012), Handbook of Teichmüller theory. Vol. III, IRMA Lectures in Mathematics and Theoretical Physics, 17, European Mathematical Society (EMS), Zürich, , .
Other articles and sources
Maryam Mirzakhani (2007) "Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces" Inventiones Mathematicae
External links
Moduli theory
Invariant theory | Moduli space | [
"Physics"
] | 4,425 | [
"Invariant theory",
"Group actions",
"Symmetry"
] |
361,814 | https://en.wikipedia.org/wiki/Sauropsida | Sauropsida (Greek for "lizard faces") is a clade of amniotes, broadly equivalent to the class Reptilia, though typically used in a broader sense to also include extinct stem-group relatives of modern reptiles and birds (which, as theropod dinosaurs, are nested within reptiles as more closely related to crocodilians than to lizards or turtles). The most popular definition states that Sauropsida is the sibling taxon to Synapsida, the other clade of amniotes which includes mammals as its only modern representatives. Although early synapsids have historically been referred to as "mammal-like reptiles", all synapsids are more closely related to mammals than to any modern reptile. Sauropsids, on the other hand, include all amniotes more closely related to modern reptiles than to mammals. This includes Aves (birds), which are recognized as a subgroup of archosaurian reptiles despite originally being named as a separate class in Linnaean taxonomy.
The base of Sauropsida forks into two main groups of "reptiles": Eureptilia ("true reptiles") and Parareptilia ("next to reptiles"). Eureptilia encompasses all living reptiles (including birds), as well as various extinct groups. Parareptilia is typically considered to be an entirely extinct group, though a few hypotheses for the origin of turtles have suggested that they belong to the parareptiles. The clades Recumbirostra and Varanopidae, traditionally thought to be lepospondyls and synapsids respectively, may also be basal sauropsids. The term "Sauropsida" originated in 1864 with Thomas Henry Huxley, who grouped birds with reptiles based on fossil evidence.
History of classification
Huxley and the fossil gaps
The term Sauropsida ("lizard faces") has a long history, and hails back to Thomas Henry Huxley, and his opinion that birds had risen from the dinosaurs. He based this chiefly on the fossils of Hesperornis and Archaeopteryx, that were starting to become known at the time. In the Hunterian lectures delivered at the Royal College of Surgeons in 1863, Huxley grouped the vertebrate classes informally into mammals, sauroids, and ichthyoids (the latter containing the anamniotes), based on the gaps in physiological traits and lack of transitional fossils that seemed to exist between the three groups. Early in the following year he proposed the names Sauropsida and Ichthyopsida for the two latter. Huxley did however include groups on the mammalian line (synapsids) like Dicynodon among the sauropsids. Thus, under the original definition, Sauropsida contained not only the groups usually associated with it today, but also several groups that today are known to be in the mammalian side of the tree.
Sauropsids redefined (Goodrich, 1916)
By the early 20th century, the fossils of Permian synapsids from South Africa had become well known, allowing palaeontologists to trace synapsid evolution in much greater detail. The term Sauropsida was taken up by E. S. Goodrich in 1916 much like Huxley's, to include lizards, birds and their relatives. He distinguished them from mammals and their extinct relatives, which he included in the sister group Theropsida (now usually replaced with the name Synapsida). Goodrich's classification thus differs somewhat from Huxley's, in which the non-mammalian synapsids (or at least the dicynodontians) fell under the sauropsids. Goodrich supported this division by the nature of the hearts and blood vessels in each group, and other features such as the structure of the forebrain. According to Goodrich, both lineages evolved from an earlier stem group, the Protosauria ("first lizards"), which included some Paleozoic amphibians as well as early reptiles predating the sauropsid/synapsid split (and thus not true sauropsids). His concept differed from modern classifications in that he considered a modified fifth metatarsal to be an apomorphy of the group, leading him to place Sauropterygia, Mesosauria and possibly Ichthyosauria and Araeoscelida in the Theropsida.
Detailing the reptile family tree
In 1956, D. M. S. Watson observed that sauropsids and synapsids diverged very early in the reptilian evolutionary history, and so he divided Goodrich's Protosauria between the two groups. He also reinterpreted the Sauropsida and Theropsida to exclude birds and mammals respectively, making them paraphyletic, unlike Goodrich's definition. Thus his Sauropsida included Procolophonia, Eosuchia, Protorosauria, Millerosauria, Chelonia (turtles), Squamata (lizards and snakes), Rhynchocephalia, Rhynchosauria, Choristodera, Thalattosauria, Crocodilia, "thecodonts" (paraphyletic basal Archosauria), non-avian dinosaurs, pterosaurs and sauropyterygians. However, his concept differed from the modern one in that reptiles without an otic notch, such as araeoscelids and captorhinids, were believed to be theropsids.
This classification supplemented, but was never as popular as, the classification of the reptiles (according to Romer's classic Vertebrate Paleontology) into four subclasses according to the positioning of temporal fenestrae, openings in the sides of the skull behind the eyes. Since the advent of phylogenetic nomenclature, the term Reptilia has fallen out of favor with many taxonomists, who have used Sauropsida in its place to include a monophyletic group containing the traditional reptiles and the birds.
Cladistic definitions
The class Reptilia has been known to be an evolutionary grade rather than a clade for as long as evolution has been recognised. Reclassifying reptiles has been among the key aims of phylogenetic nomenclature. The term Sauropsida had from the mid 20th century been used to denote a branch-based clade containing all amniote species which are not on the synapsid side of the split between reptiles and mammals. This group encompasses all now-living reptiles as well as birds, and as such is comparable to Goodrich's classification. The main difference is that better resolution of the early amniote tree has split up most of Goodrich's "Protosauria", though definitions of Sauropsida essentially identical to Huxley's (i.e. including the mammal-like reptiles) are also forwarded. Some later cladistic work has used Sauropsida more restrictively, to signify the crown group, i.e. all descendants of the last common ancestor of extant reptiles and birds. A number of phylogenetic stem, node and crown definitions have been published, anchored in a variety of fossil and extant organisms, thus there is currently no consensus of the actual definition (and thus content) of Sauropsida as a phylogenetic unit.
Some taxonomists, such as Benton (2004), have co-opted the term to fit into traditional rank-based classifications, making Sauropsida and Synapsida class-level taxa to replace the traditional Class Reptilia, while Modesto and Anderson (2004), using the PhyloCode standard, have suggested replacing the name Sauropsida with their redefinition of Reptilia, arguing that the latter is by far better known and should have priority.
Cladistic definitions of Sauropsida include:
Sauropsida as the total group of reptiles: "Reptiles plus all other amniotes more closely related to them than they are to mammals" (Gauthier, 1994). This is a branch-based total group definition. Gauthier (1994) considered turtles to be descended from parareptiles, thus defining Reptilia as a more restricted crown group encompassing diapsids and parareptiles (apart from mesosaurs, which he considered to be the most basal branch of sauropsids).
Sauropsida as a total group, synonymous with Reptilia sensu lato: "The most inclusive clade containing Lacerta agilis and Crocodylus niloticus, but not Homo sapiens" (Modesto & Anderson, 2004). This total group definition leaves the question of turtle ancestry unresolved.
Sauropsida as a broad node-based group: "The last common ancestor of mesosaurs, testudines and diapsids, and all its descendants" (Laurin & Reisz, 1995). Though formulated differently, this grouping was similar in scope and intention to the definition provided by Gauthier (1994).
Evolutionary history
Sauropsids evolved from basal amniotes approximately 320 million years ago, in the Carboniferous Period of the Paleozoic Era. In the Mesozoic Era (from about 250 million years ago to about 66 million years ago), sauropsids were the largest animals on land, in the water, and in the air. The Mesozoic is sometimes called the Age of Reptiles. In the Cretaceous–Paleogene extinction event, the large-bodied sauropsids died out in the global extinction event at the end of the Mesozoic era. With the exception of a few species of birds, the entire dinosaur lineage became extinct; in the following era, the Cenozoic, the remaining birds diversified so extensively that, today, nearly one out of every three species of land vertebrate is a bird species.
Phylogeny
The cladogram presented here illustrates the "family tree" of sauropsids, and follows a simplified version of the relationships found by M.S. Lee, in 2013. All genetic studies have supported the hypothesis that turtles (formerly categorized together with ancient anapsids) are diapsid reptiles, despite lacking any skull openings behind their eye sockets; some studies have even placed turtles among the archosaurs, though a few have recovered turtles as lepidosauromorphs instead. The cladogram below used a combination of genetic (molecular) and fossil (morphological) data to obtain its results.
Laurin & Piñeiro (2017) and Modesto (2019) proposed an alternate phylogeny of basal sauropsids. In this tree, parareptiles include turtles and are closely related to non-araeoscelidian diapsids. The family Varanopidae, otherwise included in Synapsida, is considered by Modesto a sauropsid group.
In recent studies, the "microsaur" clade Recumbirostra, historically considered lepospondyl reptiliomorphs, have been recovered as early sauropsids.
A 2024 study defines Captorhinidae and Araeoscelidia as sister groups that split off before the formation of crown amniota (synapsids and sauropsids). The same study also considers parareptiles to be polyphyletic, with some groups being closer to the crown group of reptiles than others.
Structure difference with synapsids
The last common ancestor of synapsids and Sauropsida lived at around 320mya during Carboniferous, known as Reptiliomorpha.
Thermal and secretion
The early synapsids inherited abundant glands on their skins from their amphibian ancestors. Those glands evolved into sweat glands in synapsids, which granted them the ability to maintain constant body temperature but made them unable to save water from evaporation. Moreover, the way synapsids discharge nitrogenous waste is through urea, which is toxic and must be dissolved in water to be secreted. Unfortunately, the upcoming Permian and Triassic periods were arid periods. As a result, only a small percent of early synapsids survived in the land from South Africa to Antarctica in today's geography. Unlike synapsids, sauropsids do not have those glands on the skin; their way of nitrogenous waste emission is through uric acid which does not require water and can be excreted with feces. As a result, sauropsids were able to expand to all environments and reach their pinnacle. Even today, most vertebrates that live in arid environments are sauropsids, snakes and desert lizards for example.
Brain structure
Different from how synapsids have their cortex in six different layers of neurons which is called neocortex, the cerebrum of Sauropsida has a completely different structure. For the corresponding structure of the cerebrum in the classic view, the neocortex of synapsids is homology with only the archicortex of the avian brain. However, in the modern view appeared since the 1960s, behavioral studies suggested that avian neostriatum and hyperstriatum can receive signals of vision, hearing, and body sensations, which means they act just like the neocortex. Comparing an avian brain to that to a mammal, nuclear-to-layered hypothesis proposed by Karten (1969), suggested that the cells which form layers in synapsids' neocortex, gather individually by type and form several nuclei. For synapsids, when one new function is adapted in evolution it will be assigned to a separate area of cortex, so for each function, synapsids will have to develop a separate area of cortex, and damage to that specific cortex may cause disability. However, for Sauropsida functions are disassembled and assigned to all nuclei. In this case, brain function is highly flexible for Sauropsida, even with a small brain, many Sauropsida can still have a relatively high intelligence compared to mammals, for example, birds in the family Corvidae. So, it is possible that some non-avian dinosaurs, like Tyrannosaurus, which had tiny brains compared to their enormous body size, were more intelligent than previously thought.
References
Amniotes
Extant Pennsylvanian first appearances
Fossil taxa described in 1956
Taxa named by D. M. S. Watson | Sauropsida | [
"Biology"
] | 3,025 | [
"Reptiles",
"Animals"
] |
361,897 | https://en.wikipedia.org/wiki/Astrophysics | Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space—what they are, rather than where they are", which is studied in celestial mechanics.
Among the subjects studied are the Sun (solar physics), other stars, galaxies, extrasolar planets, the interstellar medium, and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, astrophysicists apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.
In practice, modern astronomical research often involves substantial work in the realms of theoretical and observational physics. Some areas of study for astrophysicists include the properties of dark matter, dark energy, black holes, and other celestial bodies; and the origin and ultimate fate of the universe. Topics also studied by theoretical astrophysicists include Solar System formation and evolution; stellar dynamics and evolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity, special relativity, and quantum and physical cosmology (the physical study of the largest-scale structures of the universe), including string cosmology and astroparticle physics.
History
Astronomy is an ancient science, long separated from the study of terrestrial physics. In the Aristotelian worldview, bodies in the sky appeared to be unchanging spheres whose only motion was uniform motion in a circle, while the earthly world was the realm which underwent growth and decay and in which natural motion was in a straight line and ended when the moving object reached its goal. Consequently, it was held that the celestial region was made of a fundamentally different kind of matter from that found in the terrestrial sphere; either Fire as maintained by Plato, or Aether as maintained by Aristotle.
During the 17th century, natural philosophers such as Galileo, Descartes, and Newton began to maintain that the celestial and terrestrial regions were made of similar kinds of material and were subject to the same natural laws. Their challenge was that the tools had not yet been invented with which to prove these assertions.
For much of the nineteenth century, astronomical research was focused on the routine work of measuring the positions and computing the motions of astronomical objects. A new astronomy, soon to be called astrophysics, began to emerge when William Hyde Wollaston and Joseph von Fraunhofer independently discovered that, when decomposing the light from the Sun, a multitude of dark lines (regions where there was less or no light) were observed in the spectrum. By 1860 the physicist, Gustav Kirchhoff, and the chemist, Robert Bunsen, had demonstrated that the dark lines in the solar spectrum corresponded to bright lines in the spectra of known gases, specific lines corresponding to unique chemical elements. Kirchhoff deduced that the dark lines in the solar spectrum are caused by absorption by chemical elements in the Solar atmosphere. In this way it was proved that the chemical elements found in the Sun and stars were also found on Earth.
Among those who extended the study of solar and stellar spectra was Norman Lockyer, who in 1868 detected radiant, as well as dark lines in solar spectra. Working with chemist Edward Frankland to investigate the spectra of elements at various temperatures and pressures, he could not associate a yellow line in the solar spectrum with any known elements. He thus claimed the line represented a new element, which was called helium, after the Greek Helios, the Sun personified.
In 1885, Edward C. Pickering undertook an ambitious program of stellar spectral classification at Harvard College Observatory, in which a team of woman computers, notably Williamina Fleming, Antonia Maury, and Annie Jump Cannon, classified the spectra recorded on photographic plates. By 1890, a catalog of over 10,000 stars had been prepared that grouped them into thirteen spectral types. Following Pickering's vision, by 1924 Cannon expanded the catalog to nine volumes and over a quarter of a million stars, developing the Harvard Classification Scheme which was accepted for worldwide use in 1922.
In 1895, George Ellery Hale and James E. Keeler, along with a group of ten associate editors from Europe and the United States, established The Astrophysical Journal: An International Review of Spectroscopy and Astronomical Physics. It was intended that the journal would fill the gap between journals in astronomy and physics, providing a venue for publication of articles on astronomical applications of the spectroscope; on laboratory research closely allied to astronomical physics, including wavelength determinations of metallic and gaseous spectra and experiments on radiation and absorption; on theories of the Sun, Moon, planets, comets, meteors, and nebulae; and on instrumentation for telescopes and laboratories.
Around 1920, following the discovery of the Hertzsprung–Russell diagram still used as the basis for classifying stars and their evolution, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars. At that time, the source of stellar energy was a complete mystery; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation E = mc2. This was a particularly remarkable development since at that time fusion and thermonuclear energy, and even that stars are largely composed of hydrogen (see metallicity), had not yet been discovered.
In 1925 Cecilia Helena Payne (later Cecilia Payne-Gaposchkin) wrote an influential doctoral dissertation at Radcliffe College, in which she applied Saha's ionization theory to stellar atmospheres to relate the spectral classes to the temperature of stars. Most significantly, she discovered that hydrogen and helium were the principal components of stars, not the composition of Earth. Despite Eddington's suggestion, discovery was so unexpected that her dissertation readers (including Russell) convinced her to modify the conclusion before publication. However, later research confirmed her discovery.
By the end of the 20th century, studies of astronomical spectra had expanded to cover wavelengths extending from radio waves through optical, x-ray, and gamma wavelengths. In the 21st century, it further expanded to include observations based on gravitational waves.
Observational astrophysics
Observational astronomy is a division of the astronomical science that is concerned with recording and interpreting data, in contrast with theoretical astrophysics, which is mainly concerned with finding out the measurable implications of physical models. It is the practice of observing celestial objects by using telescopes and other astronomical apparatus.
Most astrophysical observations are made using the electromagnetic spectrum.
Radio astronomy studies radiation with a wavelength greater than a few millimeters. Example areas of study are radio waves, usually emitted by cold objects such as interstellar gas and dust clouds; the cosmic microwave background radiation which is the redshifted light from the Big Bang; pulsars, which were first detected at microwave frequencies. The study of these waves requires very large radio telescopes.
Infrared astronomy studies radiation with a wavelength that is too long to be visible to the naked eye but is shorter than radio waves. Infrared observations are usually made with telescopes similar to the familiar optical telescopes. Objects colder than stars (such as planets) are normally studied at infrared frequencies.
Optical astronomy was the earliest kind of astronomy. Telescopes paired with a charge-coupled device or spectroscopes are the most common instruments used. The Earth's atmosphere interferes somewhat with optical observations, so adaptive optics and space telescopes are used to obtain the highest possible image quality. In this wavelength range, stars are highly visible, and many chemical spectra can be observed to study the chemical composition of stars, galaxies, and nebulae.
Ultraviolet, X-ray and gamma ray astronomy study very energetic processes such as binary pulsars, black holes, magnetars, and many others. These kinds of radiation do not penetrate the Earth's atmosphere well. There are two methods in use to observe this part of the electromagnetic spectrum—space-based telescopes and ground-based imaging air Cherenkov telescopes (IACT). Examples of Observatories of the first type are RXTE, the Chandra X-ray Observatory and the Compton Gamma Ray Observatory. Examples of IACTs are the High Energy Stereoscopic System (H.E.S.S.) and the MAGIC telescope.
Other than electromagnetic radiation, few things may be observed from the Earth that originate from great distances. A few gravitational wave observatories have been constructed, but gravitational waves are extremely difficult to detect. Neutrino observatories have also been built, primarily to study the Sun. Cosmic rays consisting of very high-energy particles can be observed hitting the Earth's atmosphere.
Observations can also vary in their time scale. Most optical observations take minutes to hours, so phenomena that change faster than this cannot readily be observed. However, historical data on some objects is available, spanning centuries or millennia. On the other hand, radio observations may look at events on a millisecond timescale (millisecond pulsars) or combine years of data (pulsar deceleration studies). The information obtained from these different timescales is very different.
The study of the Sun has a special place in observational astrophysics. Due to the tremendous distance of all other stars, the Sun can be observed in a kind of detail unparalleled by any other star. Understanding the Sun serves as a guide to understanding of other stars.
The topic of how stars change, or stellar evolution, is often modeled by placing the varieties of star types in their respective positions on the Hertzsprung–Russell diagram, which can be viewed as representing the state of a stellar object, from birth to destruction.
Theoretical astrophysics
Theoretical astrophysicists use a wide variety of tools which include analytical models (for example, polytropes to approximate the behaviors of a star) and computational numerical simulations. Each has some advantages. Analytical models of a process are generally better for giving insight into the heart of what is going on. Numerical models can reveal the existence of phenomena and effects that would otherwise not be seen.
Theorists in astrophysics endeavor to create theoretical models and figure out the observational consequences of those models. This helps allow observers to look for data that can refute a model or help in choosing between several alternate or conflicting models.
Theorists also try to generate or modify models to take into account new data. In the case of an inconsistency, the general tendency is to try to make minimal modifications to the model to fit the data. In some cases, a large amount of inconsistent data over time may lead to total abandonment of a model.
Topics studied by theoretical astrophysicists include stellar dynamics and evolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity and physical cosmology, including string cosmology and astroparticle physics. Relativistic astrophysics serves as a tool to gauge the properties of large-scale structures for which gravitation plays a significant role in physical phenomena investigated and as the basis for black hole (astro)physics and the study of gravitational waves.
Some widely accepted and studied theories and models in astrophysics, now included in the Lambda-CDM model, are the Big Bang, cosmic inflation, dark matter, dark energy and fundamental theories of physics.
Popularization
The roots of astrophysics can be found in the seventeenth century emergence of a unified physics, in which the same laws applied to the celestial and terrestrial realms. There were scientists who were qualified in both physics and astronomy who laid the firm foundation for the current science of astrophysics. In modern times, students continue to be drawn to astrophysics due to its popularization by the Royal Astronomical Society and notable educators such as prominent professors Lawrence Krauss, Subrahmanyan Chandrasekhar, Stephen Hawking, Hubert Reeves, Carl Sagan and Patrick Moore. The efforts of the early, late, and present scientists continue to attract young people to study the history and science of astrophysics.
The television sitcom show The Big Bang Theory popularized the field of astrophysics with the general public, and featured some well known scientists like Stephen Hawking and Neil deGrasse Tyson.
See also
References
Further reading
Astrophysics, Scholarpedia Expert articles
External links
Astronomy and Astrophysics, a European Journal
Astrophysical Journal
Cosmic Journey: A History of Scientific Cosmology from the American Institute of Physics
International Journal of Modern Physics D from World Scientific
List and directory of peer-reviewed Astronomy / Astrophysics Journals
Ned Wright's Cosmology Tutorial, UCLA
Astronomical sub-disciplines | Astrophysics | [
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361,909 | https://en.wikipedia.org/wiki/Computer%20lab | A computer lab is a space where computer services are provided to a defined community. These are typically public libraries and academic institutions. Generally, users must follow a certain user policy to retain access to the computers. This usually consists of rules such as no illegal activity during use or attempts to circumvent any security or content-control software while using the computers.
Computer labs are often subject to time limits in order to allow more people access to use the lab. It is also common for personal login credentials to be required for access. This allows institutions to track the user's activities for any possible fraudulent use. The computers in computer labs are typically equipped with Internet access, scanners, and printers and are typically arranged in rows. This is to give the workstation a similar view to facilitate lecturing or presentations, and also to facilitate small group work.
For some academic institutions, student laptops or laptop carts take place of dedicated computer labs. However, computer labs still have a place in applications requiring special software or hardware which are not easily accessible in personal computers.
Purposes
While computer labs are generally multipurpose, some labs may contain computers with hardware or software optimized for certain tasks or processes, depending on the needs of the institution operating the lab. These specialized purposes may include video editing, stock trading, 3-D computer-aided design, programming, and GIS. Increasingly, these have become the main purposes for the existence of traditional desktop-style computer labs, due to rising ownership of inexpensive personal computers making use of the lab only necessary when the expensive, specialized software and more powerful computers needed to run it are required.
Arrangements
Alternatives
In some settings, traditional desktop computer labs are impractical due to the requirement of a dedicated space. Because of this, some labs use laptop carts instead of desktop setups, in order to both save space and give the lab some degree of mobility.
In the context of academic institutions, some traditional desktop computer labs are being phased out in favor of other solutions judged to be more efficient given that most students own personal laptops. One of these solutions is a virtual lab, which can allow users to install software from the lab server onto their own laptops or log into virtual machines remotely, essentially turning their own laptops into lab machines.
Academic software bundles
Many universities purchase and maintain discounted academic software bundles and software suites, or free open-source software for their computer labs, such as programming text editors, programming languages, CAx software, rendering engines, Adobe Creative Cloud, Microsoft Office Suite, productivity software, statistical software, music software, video editing software, 3D animation software, and photo editing software.
Similar spaces
Media lab
A media lab (often referred to as "new media lab" or "media research lab") is a term used for interdisciplinary organizations, collectives or spaces with the main focus on new media, digital culture and technology. The MIT Media Lab is a well-known example of a media lab.
Internet café
An Internet café is essentially a public-facing computer lab that anyone can use but which charge a fee (often hourly) to use their computers. The term 'Internet café' may be used interchangeably with 'computer lab' but may differ from a computer lab in that users can also connect to the Internet using their own device, and users of a computer lab generally do not need any equipment of their own. Moreover, in typical parlance, a computer lab is a location within a larger organization (such as a university), while an Internet café is a standalone business.
See also
Computer science
Computers in the classroom
Cubicle
School library
Kiosk software
Public computer
LAN gaming center
Fab lab
References
External links
Centralized computing
Laboratory types
Rooms
Articles containing video clips
Educational environment | Computer lab | [
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361,924 | https://en.wikipedia.org/wiki/Order%20theory | Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary.
Background and motivation
Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.g. "2 is less than 3", "10 is greater than 5", or "Does Tom have fewer cookies than Sally?". This intuitive concept can be extended to orders on other sets of numbers, such as the integers and the reals. The idea of being greater than or less than another number is one of the basic intuitions of number systems (compare with numeral systems) in general (although one usually is also interested in the actual difference of two numbers, which is not given by the order). Other familiar examples of orderings are the alphabetical order of words in a dictionary and the genealogical property of lineal descent within a group of people.
The notion of order is very general, extending beyond contexts that have an immediate, intuitive feel of sequence or relative quantity. In other contexts orders may capture notions of containment or specialization. Abstractly, this type of order amounts to the subset relation, e.g., "Pediatricians are physicians," and "Circles are merely special-case ellipses."
Some orders, like "less-than" on the natural numbers and alphabetical order on words, have a special property: each element can be compared to any other element, i.e. it is smaller (earlier) than, larger (later) than, or identical to. However, many other orders do not. Consider for example the subset order on a collection of sets: though the set of birds and the set of dogs are both subsets of the set of animals, neither the birds nor the dogs constitutes a subset of the other. Those orders like the "subset-of" relation for which there exist incomparable elements are called partial orders; orders for which every pair of elements is comparable are total orders.
Order theory captures the intuition of orders that arises from such examples in a general setting. This is achieved by specifying properties that a relation ≤ must have to be a mathematical order. This more abstract approach makes much sense, because one can derive numerous theorems in the general setting, without focusing on the details of any particular order. These insights can then be readily transferred to many less abstract applications.
Driven by the wide practical usage of orders, numerous special kinds of ordered sets have been defined, some of which have grown into mathematical fields of their own. In addition, order theory does not restrict itself to the various classes of ordering relations, but also considers appropriate functions between them. A simple example of an order theoretic property for functions comes from analysis where monotone functions are frequently found.
Basic definitions
This section introduces ordered sets by building upon the concepts of set theory, arithmetic, and binary relations.
Partially ordered sets
Orders are special binary relations. Suppose that P is a set and that ≤ is a relation on P ('relation on a set' is taken to mean 'relation amongst its inhabitants', i.e. ≤ is a subset of the cartesian product P x P). Then ≤ is a partial order if it is reflexive, antisymmetric, and transitive, that is, if for all a, b and c in P, we have that:
a ≤ a (reflexivity)
if a ≤ b and b ≤ a then a = b (antisymmetry)
if a ≤ b and b ≤ c then a ≤ c (transitivity).
A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear. By checking these properties, one immediately sees that the well-known orders on natural numbers, integers, rational numbers and reals are all orders in the above sense. However, these examples have the additional property that any two elements are comparable, that is, for all a and b in P, we have that:
a ≤ b or b ≤ a.
A partial order with this property is called a total order. These orders can also be called linear orders or chains. While many familiar orders are linear, the subset order on sets provides an example where this is not the case. Another example is given by the divisibility (or "is-a-factor-of") relation |. For two natural numbers n and m, we write n|m if n divides m without remainder. One easily sees that this yields a partial order. For example neither 3 divides 13 nor 13 divides 3, so 3 and 13 are not comparable elements of the divisibility relation on the set of integers.
The identity relation = on any set is also a partial order in which every two distinct elements are incomparable. It is also the only relation that is both a partial order and an equivalence relation because it satisfies both the antisymmetry property of partial orders and the symmetry property of equivalence relations. Many advanced properties of posets are interesting mainly for non-linear orders.
Visualizing a poset
Hasse diagrams can visually represent the elements and relations of a partial ordering. These are graph drawings where the vertices are the elements of the poset and the ordering relation is indicated by both the edges and the relative positioning of the vertices. Orders are drawn bottom-up: if an element x is smaller than (precedes) y then there exists a path from x to y that is directed upwards. It is often necessary for the edges connecting elements to cross each other, but elements must never be located within an edge. An instructive exercise is to draw the Hasse diagram for the set of natural numbers that are smaller than or equal to 13, ordered by | (the divides relation).
Even some infinite sets can be diagrammed by superimposing an ellipsis (...) on a finite sub-order. This works well for the natural numbers, but it fails for the reals, where there is no immediate successor above 0; however, quite often one can obtain an intuition related to diagrams of a similar kind.
Special elements within an order
In a partially ordered set there may be some elements that play a special role. The most basic example is given by the least element of a poset. For example, 1 is the least element of the positive integers and the empty set is the least set under the subset order. Formally, an element m is a least element if:
m ≤ a, for all elements a of the order.
The notation 0 is frequently found for the least element, even when no numbers are concerned. However, in orders on sets of numbers, this notation might be inappropriate or ambiguous, since the number 0 is not always least. An example is given by the above divisibility order |, where 1 is the least element since it divides all other numbers. In contrast, 0 is the number that is divided by all other numbers. Hence it is the greatest element of the order. Other frequent terms for the least and greatest elements is bottom and top or zero and unit.
Least and greatest elements may fail to exist, as the example of the real numbers shows. But if they exist, they are always unique. In contrast, consider the divisibility relation | on the set {2,3,4,5,6}. Although this set has neither top nor bottom, the elements 2, 3, and 5 have no elements below them, while 4, 5 and 6 have none above. Such elements are called minimal and maximal, respectively. Formally, an element m is minimal if:
a ≤ m implies a = m, for all elements a of the order.
Exchanging ≤ with ≥ yields the definition of maximality. As the example shows, there can be many maximal elements and some elements may be both maximal and minimal (e.g. 5 above). However, if there is a least element, then it is the only minimal element of the order. Again, in infinite posets maximal elements do not always exist - the set of all finite subsets of a given infinite set, ordered by subset inclusion, provides one of many counterexamples. An important tool to ensure the existence of maximal elements under certain conditions is Zorn's Lemma.
Subsets of partially ordered sets inherit the order. We already applied this by considering the subset {2,3,4,5,6} of the natural numbers with the induced divisibility ordering. Now there are also elements of a poset that are special with respect to some subset of the order. This leads to the definition of upper bounds. Given a subset S of some poset P, an upper bound of S is an element b of P that is above all elements of S. Formally, this means that
s ≤ b, for all s in S.
Lower bounds again are defined by inverting the order. For example, -5 is a lower bound of the natural numbers as a subset of the integers. Given a set of sets, an upper bound for these sets under the subset ordering is given by their union. In fact, this upper bound is quite special: it is the smallest set that contains all of the sets. Hence, we have found the least upper bound of a set of sets. This concept is also called supremum or join, and for a set S one writes sup(S) or for its least upper bound. Conversely, the greatest lower bound is known as infimum or meet and denoted inf(S) or . These concepts play an important role in many applications of order theory. For two elements x and y, one also writes and for sup({x,y}) and inf({x,y}), respectively.
For example, 1 is the infimum of the positive integers as a subset of integers.
For another example, consider again the relation | on natural numbers. The least upper bound of two numbers is the smallest number that is divided by both of them, i.e. the least common multiple of the numbers. Greatest lower bounds in turn are given by the greatest common divisor.
Duality
In the previous definitions, we often noted that a concept can be defined by just inverting the ordering in a former definition. This is the case for "least" and "greatest", for "minimal" and "maximal", for "upper bound" and "lower bound", and so on. This is a general situation in order theory: A given order can be inverted by just exchanging its direction, pictorially flipping the Hasse diagram top-down. This yields the so-called dual, inverse, or opposite order.
Every order theoretic definition has its dual: it is the notion one obtains by applying the definition to the inverse order. Since all concepts are symmetric, this operation preserves the theorems of partial orders. For a given mathematical result, one can just invert the order and replace all definitions by their duals and one obtains another valid theorem. This is important and useful, since one obtains two theorems for the price of one. Some more details and examples can be found in the article on duality in order theory.
Constructing new orders
There are many ways to construct orders out of given orders. The dual order is one example. Another important construction is the cartesian product of two partially ordered sets, taken together with the product order on pairs of elements. The ordering is defined by (a, x) ≤ (b, y) if (and only if) a ≤ b and x ≤ y. (Notice carefully that there are three distinct meanings for the relation symbol ≤ in this definition.) The disjoint union of two posets is another typical example of order construction, where the order is just the (disjoint) union of the original orders.
Every partial order ≤ gives rise to a so-called strict order <, by defining a < b if a ≤ b and not b ≤ a. This transformation can be inverted by setting a ≤ b if a < b or a = b. The two concepts are equivalent although in some circumstances one can be more convenient to work with than the other.
Functions between orders
It is reasonable to consider functions between partially ordered sets having certain additional properties that are related to the ordering relations of the two sets. The most fundamental condition that occurs in this context is monotonicity. A function f from a poset P to a poset Q is monotone, or order-preserving, if a ≤ b in P implies f(a) ≤ f(b) in Q (Noting that, strictly, the two relations here are different since they apply to different sets.). The converse of this implication leads to functions that are order-reflecting, i.e. functions f as above for which f(a) ≤ f(b) implies a ≤ b. On the other hand, a function may also be order-reversing or antitone, if a ≤ b implies f(a) ≥ f(b).
An order-embedding is a function f between orders that is both order-preserving and order-reflecting. Examples for these definitions are found easily. For instance, the function that maps a natural number to its successor is clearly monotone with respect to the natural order. Any function from a discrete order, i.e. from a set ordered by the identity order "=", is also monotone. Mapping each natural number to the corresponding real number gives an example for an order embedding. The set complement on a powerset is an example of an antitone function.
An important question is when two orders are "essentially equal", i.e. when they are the same up to renaming of elements. Order isomorphisms are functions that define such a renaming. An order-isomorphism is a monotone bijective function that has a monotone inverse. This is equivalent to being a surjective order-embedding. Hence, the image f(P) of an order-embedding is always isomorphic to P, which justifies the term "embedding".
A more elaborate type of functions is given by so-called Galois connections. Monotone Galois connections can be viewed as a generalization of order-isomorphisms, since they constitute of a pair of two functions in converse directions, which are "not quite" inverse to each other, but that still have close relationships.
Another special type of self-maps on a poset are closure operators, which are not only monotonic, but also idempotent, i.e. f(x) = f(f(x)), and extensive (or inflationary), i.e. x ≤ f(x). These have many applications in all kinds of "closures" that appear in mathematics.
Besides being compatible with the mere order relations, functions between posets may also behave well with respect to special elements and constructions. For example, when talking about posets with least element, it may seem reasonable to consider only monotonic functions that preserve this element, i.e. which map least elements to least elements. If binary infima ∧ exist, then a reasonable property might be to require that f(x ∧ y) = f(x) ∧ f(y), for all x and y. All of these properties, and indeed many more, may be compiled under the label of limit-preserving functions.
Finally, one can invert the view, switching from functions of orders to orders of functions. Indeed, the functions between two posets P and Q can be ordered via the pointwise order. For two functions f and g, we have f ≤ g if f(x) ≤ g(x) for all elements x of P. This occurs for example in domain theory, where function spaces play an important role.
Special types of orders
Many of the structures that are studied in order theory employ order relations with further properties. In fact, even some relations that are not partial orders are of special interest. Mainly the concept of a preorder has to be mentioned. A preorder is a relation that is reflexive and transitive, but not necessarily antisymmetric. Each preorder induces an equivalence relation between elements, where a is equivalent to b, if a ≤ b and b ≤ a. Preorders can be turned into orders by identifying all elements that are equivalent with respect to this relation.
Several types of orders can be defined from numerical data on the items of the order: a total order results from attaching distinct real numbers to each item and using the numerical comparisons to order the items; instead, if distinct items are allowed to have equal numerical scores, one obtains a strict weak ordering. Requiring two scores to be separated by a fixed threshold before they may be compared leads to the concept of a semiorder, while allowing the threshold to vary on a per-item basis produces an interval order.
An additional simple but useful property leads to so-called well-founded, for which all non-empty subsets have a minimal element. Generalizing well-orders from linear to partial orders, a set is well partially ordered if all its non-empty subsets have a finite number of minimal elements.
Many other types of orders arise when the existence of infima and suprema of certain sets is guaranteed. Focusing on this aspect, usually referred to as completeness of orders, one obtains:
Bounded posets, i.e. posets with a least and greatest element (which are just the supremum and infimum of the empty subset),
Lattices, in which every non-empty finite set has a supremum and infimum,
Complete lattices, where every set has a supremum and infimum, and
Directed complete partial orders (dcpos), that guarantee the existence of suprema of all directed subsets and that are studied in domain theory.
Partial orders with complements, or poc sets, are posets with a unique bottom element 0, as well as an order-reversing involution such that
However, one can go even further: if all finite non-empty infima exist, then ∧ can be viewed as a total binary operation in the sense of universal algebra. Hence, in a lattice, two operations ∧ and ∨ are available, and one can define new properties by giving identities, such as
x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z), for all x, y, and z.
This condition is called distributivity and gives rise to distributive lattices. There are some other important distributivity laws which are discussed in the article on distributivity in order theory. Some additional order structures that are often specified via algebraic operations and defining identities are
Heyting algebras and
Boolean algebras,
which both introduce a new operation ~ called negation. Both structures play a role in mathematical logic and especially Boolean algebras have major applications in computer science.
Finally, various structures in mathematics combine orders with even more algebraic operations, as in the case of quantales, that allow for the definition of an addition operation.
Many other important properties of posets exist. For example, a poset is locally finite if every closed interval [a, b] in it is finite. Locally finite posets give rise to incidence algebras which in turn can be used to define the Euler characteristic of finite bounded posets.
Subsets of ordered sets
In an ordered set, one can define many types of special subsets based on the given order. A simple example are upper sets; i.e. sets that contain all elements that are above them in the order. Formally, the upper closure of a set S in a poset P is given by the set {x in P | there is some y in S with y ≤ x}. A set that is equal to its upper closure is called an upper set. Lower sets are defined dually.
More complicated lower subsets are ideals, which have the additional property that each two of their elements have an upper bound within the ideal. Their duals are given by filters. A related concept is that of a directed subset, which like an ideal contains upper bounds of finite subsets, but does not have to be a lower set. Furthermore, it is often generalized to preordered sets.
A subset which is - as a sub-poset - linearly ordered, is called a chain. The opposite notion, the antichain, is a subset that contains no two comparable elements; i.e. that is a discrete order.
Related mathematical areas
Although most mathematical areas use orders in one or the other way, there are also a few theories that have relationships which go far beyond mere application. Together with their major points of contact with order theory, some of these are to be presented below.
Universal algebra
As already mentioned, the methods and formalisms of universal algebra are an important tool for many order theoretic considerations. Beside formalizing orders in terms of algebraic structures that satisfy certain identities, one can also establish other connections to algebra. An example is given by the correspondence between Boolean algebras and Boolean rings. Other issues are concerned with the existence of free constructions, such as free lattices based on a given set of generators. Furthermore, closure operators are important in the study of universal algebra.
Topology
In topology, orders play a very prominent role. In fact, the collection of open sets provides a classical example of a complete lattice, more precisely a complete Heyting algebra (or "frame" or "locale"). Filters and nets are notions closely related to order theory and the closure operator of sets can be used to define a topology. Beyond these relations, topology can be looked at solely in terms of the open set lattices, which leads to the study of pointless topology. Furthermore, a natural preorder of elements of the underlying set of a topology is given by the so-called specialization order, that is actually a partial order if the topology is T0.
Conversely, in order theory, one often makes use of topological results. There are various ways to define subsets of an order which can be considered as open sets of a topology. Considering topologies on a poset (X, ≤) that in turn induce ≤ as their specialization order, the finest such topology is the Alexandrov topology, given by taking all upper sets as opens. Conversely, the coarsest topology that induces the specialization order is the upper topology, having the complements of principal ideals (i.e. sets of the form {y in X | y ≤ x} for some x) as a subbase. Additionally, a topology with specialization order ≤ may be order consistent, meaning that their open sets are "inaccessible by directed suprema" (with respect to ≤). The finest order consistent topology is the Scott topology, which is coarser than the Alexandrov topology. A third important topology in this spirit is the Lawson topology. There are close connections between these topologies and the concepts of order theory. For example, a function preserves directed suprema if and only if it is continuous with respect to the Scott topology (for this reason this order theoretic property is also called Scott-continuity).
Category theory
The visualization of orders with Hasse diagrams has a straightforward generalization: instead of displaying lesser elements below greater ones, the direction of the order can also be depicted by giving directions to the edges of a graph. In this way, each order is seen to be equivalent to a directed acyclic graph, where the nodes are the elements of the poset and there is a directed path from a to b if and only if a ≤ b. Dropping the requirement of being acyclic, one can also obtain all preorders.
When equipped with all transitive edges, these graphs in turn are just special categories, where elements are objects and each set of morphisms between two elements is at most singleton. Functions between orders become functors between categories. Many ideas of order theory are just concepts of category theory in small. For example, an infimum is just a categorical product. More generally, one can capture infima and suprema under the abstract notion of a categorical limit (or colimit, respectively). Another place where categorical ideas occur is the concept of a (monotone) Galois connection, which is just the same as a pair of adjoint functors.
But category theory also has its impact on order theory on a larger scale. Classes of posets with appropriate functions as discussed above form interesting categories. Often one can also state constructions of orders, like the product order, in terms of categories. Further insights result when categories of orders are found categorically equivalent to other categories, for example of topological spaces. This line of research leads to various representation theorems, often collected under the label of Stone duality.
History
As explained before, orders are ubiquitous in mathematics. However, the earliest explicit mentionings of partial orders are probably to be found not before the 19th century. In this context the works of George Boole are of great importance. Moreover, works of Charles Sanders Peirce, Richard Dedekind, and Ernst Schröder also consider concepts of order theory.
Contributors to ordered geometry were listed in a 1961 textbook:
In 1901 Bertrand Russell wrote "On the Notion of Order" exploring the foundations of the idea through generation of series. He returned to the topic in part IV of The Principles of Mathematics (1903). Russell noted that binary relation aRb has a sense proceeding from a to b with the converse relation having an opposite sense, and sense "is the source of order and series." (p 95) He acknowledges Immanuel Kant was "aware of the difference between logical opposition and the opposition of positive and negative". He wrote that Kant deserves credit as he "first called attention to the logical importance of asymmetric relations."
The term poset as an abbreviation for partially ordered set is attributed to Garrett Birkhoff in the second edition of his influential book Lattice Theory.
See also
Causal Sets
Cyclic order
Hierarchy
Incidence algebra
Notes
References
External links
Orders at ProvenMath partial order, linear order, well order, initial segment; formal definitions and proofs within the axioms of set theory.
Nagel, Felix (2013). Set Theory and Topology. An Introduction to the Foundations of Analysis
Organization | Order theory | [
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] | 5,498 | [
"Order theory"
] |
361,927 | https://en.wikipedia.org/wiki/Triforce | The is a fictional artifact and icon of Nintendo's The Legend of Zelda video game franchise. It first appeared in the original The Legend of Zelda video game (1986) and has appeared in every subsequent game in the series. It consists of three equilateral triangles that are joined to form a large equilateral triangle. In-universe, it represents the essences of the Golden Goddesses—Din, Nayru and Farore—who created Hyrule. Imbued with divine power, it is capable of granting any wish to anyone who possesses it.
The three pieces of the Triforce are often in the possession of the three main characters of the series, Ganon, Zelda and Link, who each embody one of its virtues: power, wisdom and courage. Obtaining the Triforce is a frequent objective in the series, requiring the player to search for its shards and protect it from Ganon, who seeks its power for evil purposes.
The Triforce is a central motif of The Legend of Zelda series, frequently appearing in Zelda iconography and merchandise. It has appeared in related media, including manga, video games and an animated television series. Due to its prominence and significance within the mythology of the Zelda series, the Triforce has become a widely recognizable symbol in gaming.
Background
Although the Triforce has become associated with The Legend of Zelda series, an identical symbol originated nearly 1,000 years before in medieval Japan. The symbol takes historical reference from the Hōjō clan, a family that took control of Japan in the 13th century. Its emblem (mon) was the mitsuuroko, or "three scales". The symbol also appears frequently in contemporary Japanese culture. It appears on the logos for large and small businesses and can be found on temples and family memorials. Since the release of The Legend of Zelda video game in 1986, the Triforce has become a recognizable icon of The Legend of Zelda series, appearing in every game in some form, particularly as part of the heraldry of the Kingdom of Hyrule.
Concept and creation
Shigeru Miyamoto, creator of The Legend of Zelda series, explained his vision for the first game in an interview with Gamekult. He said that the Triforce fragments were originally supposed to be electronic chips, as the game was intended to be set in both the past and the future. This early futuristic concept was abandoned and replaced by a heroic fantasy. In The Legend of Zelda video game, the Triforce was simply described as magical triangles of great power, but its significance was expanded in subsequent games. The first game established it as an object of desire and a central plot device that binds the three characters. Initially comprising two pieces, the third piece, the Triforce of Courage, was introduced in Zelda II: The Adventure of Link.
Characteristics
The Triforce consists of three equilateral triangles that are joined to create a large equilateral triangle. Its design resembles the Sierpiński triangle. The three pieces are the Triforce of Power, the Triforce of Wisdom, and the Triforce of Courage, which represent the qualities of the Golden Goddesses: Din, the Goddess of Power; Nayru, the Goddess of Wisdom; and Farore, the Goddess of Courage. In the creation myth of the series, they created Hyrule and the Triforce and entrusted both to the Goddess Hylia. As a divine relic infused with the power of the goddesses, the Triforce is an object of limitless power, capable of granting any wish to anyone who touches it. Its place of origin is known as the Sacred Realm.
The Triforce can only be wielded by someone who possesses a balance of the three virtues in their heart: power, wisdom and courage. Conversely, if held by someone with an imbalanced heart, it splits into three pieces, with each piece bestowed on a person who represents that quality. The three virtues of the Triforce are often distributed amongst the series' three main characters: Ganon, Princess Zelda, and Link. In some Zelda games, it manifests as a symbol on the hand of the bearer of one of the pieces. The trinity within the Triforce creates a moral balance, with evil seeking power, and wisdom and courage being the opposing forces for good. A recurring theme of the series is Ganon's plan to steal the Triforce from the Sacred Realm in order to use its power to conquer Hyrule, which is ultimately thwarted by Link and Zelda. This places the three characters in an endless battle that is repeated across the fictional timeline within a reincarnation cycle.
Appearances
The Legend of Zelda series
The Triforce is a common symbol found in the series. It is connected with the Royal Family of Hyrule and displayed as part of the Hyrule Royal Family's signature crest, which combines the Triforce with a fictional bird called a Crimson Loftwing. It is also found on various objects within the games such as the Master Sword and the Hylian Shield and on sacred sites, such as the Temple of Time.
In 1986, the original The Legend of Zelda video game introduced the Triforce, which consisted of two pieces, as a central plot device. It involves the hero, Link, embarking on a quest to save Hyrule from the evil Ganon, who has stolen the Triforce of Power. After Princess Zelda splits the Triforce of Wisdom into eight fragments and scatters them across the land, Link must search for the fragments and reassemble them to rescue Princess Zelda and defeat Ganon.
Zelda II: The Adventure of Link (1987) established the Triforce of Courage as the third piece of the Triforce. The game's instruction manual tells the backstory of Princess Zelda being placed in a magical sleep by a wizard and sets Link's fate as the hero who will wake her by marking the back of his hand with the Triforce. The story involves Link obtaining six crystals and then claiming the Triforce of Courage from the Great Palace. Using the three pieces of the Triforce, he is able to awaken sleeping Zelda from her curse.
The third game in the series titled A Link to the Past (1991) introduces a detailed fictional lore for the Triforce. In Japan, it was released with the title Triforce of the Gods. The game's instruction booklet provides the creation myth explaining how three Golden Goddesses named Din, Nayru, and Farore descended to create the land of Hyrule and then created the Triforce and imbued it with the essence of their power. In the game's backstory, Ganon enters the Sacred Realm to steal the Triforce and plunges it into darkness, creating the Dark World. To prevent Ganon from escaping and destroying the Light World, Link saves Zelda and the Sages. In the final scenes, he uses the Triforce to wish for the characters in the game to be restored.
Ganon, in his humanoid form of Ganondorf, again pursues his goal of obtaining the Triforce in Ocarina of Time (1998). Ganondorf manages to gain entry to the Sacred Realm and takes over Hyrule, plunging it into chaos. After a seven-year sleep, Link awakens as an adult and sets off to protect the Triforce from Ganondorf by travelling back and forth in time. With the help of Seven Sages, he successfully defeats Ganondorf by sealing him in the Sacred Realm. The game established the trinity of the characters each embodying one of the virtues of the Triforce.
When the game duo titled The Legend of Zelda: Oracle of Seasons and Oracle of Ages (2001) were conceived, they were originally intended to be a trilogy, with each story centred on one of the three virtues of the Triforce. In each game the Triforce initiates the adventure by summoning Link and transporting him to the worlds of Holodrum and Labrynna to collect eight Essences of Nature or Time in order to defeat the games' villains, Onox and Veran.
In The Wind Waker (2002), Link must collect eight pieces of the Triforce of Courage, which are scattered across the islands on the map, before he is ready to confront Ganondorf. The Triforce hunt, which was described by GameSpot as "infamous", is a lengthy process involving finding the chart locations, returning to Tingle and then finding the Triforce shards. Due to the tedious nature of the task, it was later simplified in The Wind Waker HD. In the finale, Ganondorf unites the Triforce, but before he can make his wish to rule Hyrule, the King of Hyrule's spirit touches it and wishes for Hyrule to be destroyed, resulting in a final battle between Ganondorf, Link and Zelda.
The Triforce does not play a major role in Twilight Princess (2006). At the beginning of the game, each of the three main characters is shown to be in possession of their individual component by glowing triangles that appear on their hands, but otherwise the Triforce only appears on murals and buildings.
Skyward Sword (2011) again focuses on the creation of the Triforce by the three Goddesses. In the game's backstory, demonic creatures rise from cracks in the earth led by Demonic King Demise with the intention of claiming the Triforce. To protect it, the goddess Hylia commands an army of the world's people to fight Demise. She seals him away and after becoming mortal, sends the humans to live above the surface world in Skyloft. She hides the Triforce in the sky to await the hero, Link, who recovers the three Triforce pieces from the Sky Keep and uses its powers to defeat Demise.
In A Link Between Worlds (2013), another version of the Triforce was introduced in the fictional universe. In Japan, the game is known as Triforce of the Gods 2, as it is a spiritual sequel to A Link to the Past. It takes place in two mirrored worlds, the Light World (Hyrule) and the Dark World (Lorule). Unlike Hyrule, Lorule has crumbled, caused by its people destroying its own Triforce, due to it being the cause of war. To save her world, Princess Hilda plots to steal Hyrule's Triforce. By the end of the game, she sympathises with Hyrule and allows Link and Zelda to return there with their Triforce. In an act of compassion, the two use the Hyrulean Triforce to recreate Lorule's Triforce.
Nintendo published Tri Force Heroes (2015) for the 3DS, a cooperative multiplayer game involving three Links dressed in red, blue and green. Hiromasa Shikata, the game's director, explained that the concept for the game was a "triangular relationship between three players".
Despite its prominence in the Zelda series, the Triforce plays no part in the storyline of Breath of the Wild (2017). It appears in various places within the game and manifests itself on the hand of Zelda in the battle against Calamity Ganon. The three virtues of the Triforce are present in the form of three springs located in different regions of the map, namely the Spring of Power, the Spring of Wisdom and the Spring of Courage. The Triforce continued to be absent from the series as a plot device with the release of Tears of the Kingdom (2023), although it appears on in-game architecture and as a tattoo on the arm of the character Sonia. This led to speculation amongst players that it has been abandoned as a major element of the series.
In Echoes of Wisdom (2024), the Triforce appears again but is described as "Prime Energy". In a Famitsu interview, Aonuma explained that he decided to "bring out the Triforce" because it was necessary for the story. The development team knew that the game would end with obtaining the Triforce but felt that its image was too strong. For this reason, they set the story in an undefined time period to give the impression that the inhabitants had forgotten the Triforce and had only a vague idea of its existence.
Television series
In The Legend of Zelda animated series the Triforce consists of two pieces, with Ganon possessing the Triforce of Power and Zelda possessing the Triforce of Wisdom. The plot of each episode revolves around Ganon's attempts to gain control of both Triforce pieces so that he can become the ruler of Hyrule. The series gave the Wisdom and Power pieces a voice and a role in the story. Phil Harnage, one of the show's writers explained that this dialogue was used to explain the show's events. The cartoon's voice cast included Elizabeth Hanna as the Triforce of Wisdom and Allen Stewart-Coates as the Triforce of Power.
Manga and comics
Following the release of The Legend of Zelda video game, a companion manga book titled The Hyrule Fantasy was released in Japan by Wanpaku Comics in September 1986. It follows the game's story, involving the eight fragments of the Triforce. In 1992, a Choose Your Own Adventure-style book was released in Japanese titled The Legend of Zelda: The Triforce of the Gods. It was based on A Link to the Past, though some story elements deviated from the game. Two manga adaptations of A Link to the Past were also published by Ataru Cagiva in 1995 and Akira Himekawa in 2005 with the Japanese title Triforce of the Gods. Akira Himekawa also produced a manga book published by Viz Media, which is based on Ocarina of Time and follows the game's plot involving Link's quest to protect the Triforce from Ganondorf. In the early 1990s, Valiant Comics published The Legend of Zelda comic book based on the animated series. In the third issue, Link is corrupted by the Triforce of Power and attacks Zelda to obtain the Triforce of Wisdom. In the fifth issue, the second storyline is titled "The Day of the Triforce", which involves Link battling without his Triforce power due to its disappearance.
Video games
The Triforce has appeared in various other video games. In the series spin-off hack and slash video game Hyrule Warriors (2014), the Triforce is the objective for one of the main antagonists, Cia. Originally a guardian of the Triforce, she is corrupted by Ganon after displaying affections for Link and builds an army to obtain the Triforce. It also appears in the Super Smash Bros. series. In Super Smash Bros. Brawl Link uses the Triforce in his final smash. In Super Smash Bros for Nintendo 3DS and Wii U, Link's and Toon Link's final smash is the Triforce Slash, which traps enemies in the Triforce before relentlessly slashing at them. In Super Smash Bros. Ultimate, the Triforce Slash appears in Toon Link's and Young Link's "Final Smash" attack. In the same game, Zelda uses the Triforce of Wisdom as her Final Smash, which produces a glowing triangle that sucks in opponents and deals damage. In Sonic Lost Worlds The Legend of Zelda DLC stage, Sonic the Hedgehog travels through Hyrule in search of the Triforce. In Mario Kart 8s The Legend of Zelda × Mario Kart 8 expansion pack and its enhanced Nintendo Switch port, one of the grand prix cups is known as the "Triforce Cup" with custom vehicle parts including the Triforce Tires. The Triforce was used in Splatoon 3 by Nintendo to promote Tears of the Kingdom prior to its release in May 2023. In the Triforce Splatfest, players were asked to choose Power, Wisdom or Courage as their team. The Tricolor Turf War was fought on a triangular map to represent the shape of the Triforce.
Other media
In 2017, Nintendo rolled out an escape room experience across eight cities in North America titled "Defenders of the Triforce".
"Triforce" is also a name given to an arcade board system that was a joint venture from three companies; Namco, Nintendo and Sega using a combination of Nintendo GameCube and Sega GD-ROM hardware inside a Namco cabinet.
In popular culture
The Triforce has been used as a shibboleth and a meme to embarrass newer users of the imageboard website 4chan. Experienced users write it using Unicode characters, but copying and pasting the Triforce results in the symbol becoming misaligned.
Due to its simple design and popularity with gamers, the Triforce has become one of the most popular gaming tattoos. Professional wrestler Cody Rhodes, a longtime Legend of Zelda fan, formerly had the Triforce on his wrestling boots in his early career with the WWE.
The Triforce has inspired the production of Zelda-themed products, including a beer named Triforce IPA.
In 2023, the British metal band DragonForce released a single titled "Power of the Triforce", which is a tribute to The Legend of Zelda series.
Merchandise
The Triforce regularly appears on official Zelda merchandise, including clothing and accessories. It is prominently displayed on the cover of The Legend of Zelda Encyclopedia, which is published by Dark Horse. In 2023, it was recreated as a logic puzzle for Nintendo by a Japanese toy manufacturer. Images of the Triforce appear on a set of official t-shirts that were released for the Triforce-themed Splatfest.
Reception
The Triforce has become a recognisable icon of The Legend of Zelda series. It has been carved into headstones and used as a family crest. Brian Ashcraft of Kotaku commented that, although the inspiration for the Triforce is unknown, the symbol is found on the grave of Japanese video game designer Gunpei Yokoi, creator of the Game Boy, as his family crest or "kamon" (家紋). Florent Gorges, author of The History of Nintendo, opined that the symbol is so ubiquitous in Japan that Yokoi's protégé, Shigeru Miyamoto, could not have ignored it and had reused the design for the Zelda series. Ashcraft also remarked that the Triforce had such an impact on the younger Japanese generation, that the crest is now widely recognised, not as the mitsuuroko symbol, but as the icon of The Legend of Zelda series. In 1999, the Triforce in Ocarina of Time became the centre of a hoax, where a user account successfully convinced the Zelda fandom that the Triforce could be acquired, by posting a series of fake hints that were eventually debunked. Kotaku described it as "one of the greatest hoaxes in video game history". In 2016, Kate Gray of TechRadar noted that players persisted in their search for the Triforce in Ocarina of Time, using various methods of play in the hope of recovering it.
Stephen Totilo, writing for Kotaku, highlighted that in 2016 Zelda series producer Eiji Aonuma used the Triforce to reinforce the fixed gender roles of the three main characters in the series. Aonuma stated that the concept of creating a female version of Link, "would mess with the balance of the Triforce" and had been rejected by Nintendo for that reason. Jacob Kastrenakes of The Verge strongly disagreed by commenting that, although the three characters possess and embody the three virtues of the Triforce, the pieces could "theoretically be held by others in Hyrule" and that none of the Triforce pieces relate to gender.
The Triforce has been the subject of interpretation with regards to its significance within the Zelda series. Luke Cuddy considered that the Triforce can be interpreted as a lesson in morality that can be applied in the real world, as each of the three Triforce pieces is equal and could be used by the three main characters for good or evil, depending on how they choose to act. Anthony Bean opined that the Triforce is a symbol of the self in Jungian psychology, because it "serves as a connection between Hyrule (the conscious, mortal realm) and the goddesses (the unconscious, divine realm) just as the self serves as a meeting point for the ego and the unconscious". Edge staff commented that the Triforce is the deus ex machina of The Legend of Zelda series, stating that, of all the world-saving devices in gaming, it is "the most visually iconic and symbolically potent one" and noted its Christian similarities: "salvation through a trinity that is also one".
Luke Plunkett of Kotaku opined that the Triforce is "one of the most iconic designs in the history of video games" and "the object that lies at the heart of The Legend of Zelda". Eurogamer staff commented that the Triforce symbolises "Zelda's perpetually cycling legend" and is the blueprint for every game in the series, with Link representing "agency, curiosity, the eternal innocence", Ganon representing "selfishness, megalomania, destruction" and Zelda representing "insight and direction". Nicole Carpenter for Polygon commented that the Triforce has become a ubiquitous symbol that is widely recognised amongst gamers. She highlighted that it creates a sense of community for many isolated gamers and also provides personal significance to those who find comfort and meaning in its symbolism.
See also
Sierpiński triangle
References
Fictional elements introduced in 1986
Magic items
The Legend of Zelda
Video game objects
ca:Triforce
simple:Triforce
sv:Trekraft | Triforce | [
"Physics"
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361,933 | https://en.wikipedia.org/wiki/Strut | A strut is a structural component commonly found in engineering, aeronautics, architecture and anatomy. Struts generally work by resisting longitudinal compression, but they may also serve in tension.
A stay is sometimes used as a synonym for strut, but some sources distinguish that struts are braces for holding compressive forces apart, while stays are braces for keeping stretching forces together.
Human anatomy
Part of the functionality of the clavicle is to serve as a strut between the scapula and sternum, resisting forces that would otherwise bring the upper limb close to the thorax. Keeping the upper limb away from the thorax is vital for its range of motion. Complete lack of clavicles may be seen in cleidocranial dysostosis, and the abnormal proximity of the shoulders to the median plane in cases of this genetic condition exemplifies the clavicle's importance as a strut.
Architecture and construction
Strut is a common name in timber framing for a support or brace of scantlings lighter than a post. Frequently struts are found in roof framing from either a tie beam or a king post to a principal rafter. Struts may be vertically plumb or leaning (then called canted, raking, or angled) and may be straight or curved. In the U.K., strut is generally used in a sense of a lighter duty piece: a king post carries a ridge beam but a king strut does not, a queen post carries a plate but a queen strut does not, a crown post carries a crown plate but a crown strut does not.
Strutting or blocking between floor joists adds strength to the floor system.
Struts provide outwards-facing support in their lengthwise direction, which can be used to keep two other components separate, performing the opposite function of a tie.
In piping, struts restrain movement of a component in one direction while allowing movement or contraction in another direction.
Strut channel made from steel, aluminium, or fibre-reinforced plastic is used heavily in the building industry and is often used in the support of cable trays and other forms of cable management, and pipes support systems.
Aircraft
Bracing struts and wires of many kinds were extensively used in early aircraft to stiffen and strengthen, and sometimes even to form, the main functional airframe. Throughout the 1920s and 1930s they fell out of use in favour of the low drag cantilever construction. Most aircraft bracing struts are principally loaded in compression, with wires taking the tension loads. Lift struts came into increasing use during the changeover period and remain in use on smaller aircraft today where ultimate performance is not an issue. Typically, they are applied to a high wing monoplane and act in tension during flight.
Struts have also been widely used for purely structural reasons to attach engines, landing gear and other loads. The oil-sprung legs of retractable landing gear are still called Oleo struts.
Automobiles
As components of an automobile chassis, struts can be passive braces to reinforce the chassis and/or body, or active components of the suspension. An example of an active unit would be a coilover design in an automotive suspension. The coilover combines a shock absorber and a spring in a single unit.
A common form of automotive suspension strut in an automobile is the MacPherson strut. MacPherson struts are often purchased by the automakers in sets of four completed sub-assemblies: These can be mounted on the car bodies as part of the manufacturers' own assembly operations. A MacPherson strut combines the primary function of a shock absorber (as a damper), with the ability to support sideways loads not along its axis of compression, somewhat similar to a sliding pillar suspension, thus eliminating the need for an upper suspension arm. This means that a strut must have a more rugged design, with mounting points near its middle for attachment of such loads.
Another common type of strut used in air suspension is an air strut which combines the shock absorber with an air spring and can be designed in the same fashion as a coilover device. These come available in most types of suspension setups including beam axle and MacPherson strut style design.
Transportation-related struts are used in "load bearing" applications ranging from both highway and off-road suspensions to automobile hood and hatch window supports to aircraft wing supports. The majority of struts feature a bearing, but only for the cases, when the strut mounts operate as steering pivots. For such struts, the bearing is the wear item, as it is subject to constant impact of vibration and its condition reflects both wheel alignment and steering response. In vehicle suspension systems, struts are most commonly an assembly of coil-over spring and shock absorber. Other variants to using a coil-over spring as the compressible load bearer include support via pressurized nitrogen gas acting as the spring, and rigid (hard tail) support which provides neither longitudinal compression/extension nor damping.
History
Struts were created in the 1970s in which automakers transitioned from large rear-wheeled drive vehicles to more fuel-efficient front-wheeled drive vehicles. The entire suspension system was changed in accordance to meet the new style of vehicles. The new styles of vehicles left less room for the traditional system, which was called the short-arm/ long-arm suspension systems. This caused the MacPherson strut system to become the new standard for all automobiles including front-wheeled and rear-wheeled vehicles. The MacPherson strut system does not require an upper control arm, bushings, or a pivot shaft like previous models.
Options on vehicles
Struts are not necessarily needed components on vehicles which separate the springs and shock absorbers, while the shocks support no weight. There are also some vehicles with the option of only having one pair of struts on one set of wheels while the other pair uses a separate selection of shocks and springs. This singular pair of struts are almost always a MacPherson strut. These choices are made for various reasons including the balance of initial cost, performance, and other elements. Some vehicles use a "double wishbone," suspension system which exclusively uses shock absorbers. Sports cars seem to favor this suspension style; however, the Porsche 911 favors traditional struts.
Maintenance
Struts keeps your suspension aligned, along with numerous other functions. To check if a set of struts is failing; simply walk to each side of the wheel and begin to bounce the car up and down. As the car is pushed down, let it bounce back into position. If it continues to bounce up and down, consider taking your vehicle to a mechanic for replacement. You can also check your strut car to see if it's leaking oil. Bad struts could possibly lead to many issues including the breaking of a wheel, flattening of a tire, damaged power steering, broken springs, broken joints, and many more issues in your suspension system. Keep all of these in mind as you drive your vehicle with bad struts.
Gallery
See also
Cabane strut
Chapman strut
Jury strut
Lift strut
Spacers and standoffs
Strut bar
References
Automotive suspension technologies
Timber framing
ja:ストラット式サスペンション | Strut | [
"Technology"
] | 1,515 | [
"Structural system",
"Timber framing"
] |
361,940 | https://en.wikipedia.org/wiki/Idempotent%20%28ring%20theory%29 | In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element such that . That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that for any positive integer . For example, an idempotent element of a matrix ring is precisely an idempotent matrix.
For general rings, elements idempotent under multiplication are involved in decompositions of modules, and connected to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which all elements are idempotent under both addition and multiplication.
Examples
Quotients of Z
One may consider the ring of integers modulo , where is square-free. By the Chinese remainder theorem, this ring factors into the product of rings of integers modulo , where is prime. Now each of these factors is a field, so it is clear that the factors' only idempotents will be and . That is, each factor has two idempotents. So if there are factors, there will be idempotents.
We can check this for the integers , . Since has two prime factors ( and ) it should have idempotents.
From these computations, , , , and are idempotents of this ring, while and are not. This also demonstrates the decomposition properties described below: because , there is a ring decomposition . In the multiplicative identity is and in the multiplicative identity is .
Quotient of polynomial ring
Given a ring and an element such that , the quotient ring
has the idempotent . For example, this could be applied to , or any polynomial .
Idempotents in the ring of split-quaternions
There is a circle of idempotents in the ring of split-quaternions. Split quaternions have the structure of a real algebra, so elements can be written w + xi + yj + zk over a basis {1, i, j, k}, with j2 = k2 = +1. For any θ,
satisfies s2 = +1 since j and k satisfy the anticommutative property. Now
the idempotent property.
The element s is called a hyperbolic unit and so far, the i-coordinate has been taken as zero. When this coordinate is non-zero, then there is a hyperboloid of one sheet of hyperbolic units in split-quaternions. The same equality shows the idempotent property of where s is on the hyperboloid.
Types of ring idempotents
A partial list of important types of idempotents includes:
Two idempotents and are called orthogonal if . If is idempotent in the ring (with unity), then so is ; moreover, and are orthogonal.
An idempotent in is called a central idempotent if for all in , that is, if is in the center of .
A trivial idempotent refers to either of the elements and , which are always idempotent.
A primitive idempotent of a ring is a nonzero idempotent such that is indecomposable as a right -module; that is, such that is not a direct sum of two nonzero submodules. Equivalently, is a primitive idempotent if it cannot be written as , where and are nonzero orthogonal idempotents in .
A local idempotent is an idempotent such that is a local ring. This implies that is directly indecomposable, so local idempotents are also primitive.
A right irreducible idempotent is an idempotent for which is a simple module. By Schur's lemma, is a division ring, and hence is a local ring, so right (and left) irreducible idempotents are local.
A centrally primitive idempotent is a central idempotent that cannot be written as the sum of two nonzero orthogonal central idempotents.
An idempotent in the quotient ring is said to lift modulo if there is an idempotent in such that .
An idempotent of is called a full idempotent if .
A separability idempotent; see Separable algebra.
Any non-trivial idempotent is a zero divisor (because with neither nor being zero, where ). This shows that integral domains and division rings do not have such idempotents. Local rings also do not have such idempotents, but for a different reason. The only idempotent contained in the Jacobson radical of a ring is .
Rings characterized by idempotents
A ring in which all elements are idempotent is called a Boolean ring. Some authors use the term "idempotent ring" for this type of ring. In such a ring, multiplication is commutative and every element is its own additive inverse.
A ring is semisimple if and only if every right (or every left) ideal is generated by an idempotent.
A ring is von Neumann regular if and only if every finitely generated right (or every finitely generated left) ideal is generated by an idempotent.
A ring for which the annihilator every subset of is generated by an idempotent is called a Baer ring. If the condition only holds for all singleton subsets of , then the ring is a right Rickart ring. Both of these types of rings are interesting even when they lack a multiplicative identity.
A ring in which all idempotents are central is called an abelian ring. Such rings need not be commutative.
A ring is directly irreducible if and only if and are the only central idempotents.
A ring can be written as with each a local idempotent if and only if is a semiperfect ring.
A ring is called an SBI ring or Lift/rad ring if all idempotents of lift modulo the Jacobson radical.
A ring satisfies the ascending chain condition on right direct summands if and only if the ring satisfies the descending chain condition on left direct summands if and only if every set of pairwise orthogonal idempotents is finite.
If is idempotent in the ring , then is again a ring, with multiplicative identity . The ring is often referred to as a corner ring of . The corner ring arises naturally since the ring of endomorphisms .
Role in decompositions
The idempotents of have an important connection to decomposition of -modules. If is an -module and is its ring of endomorphisms, then if and only if there is a unique idempotent in such that and . Clearly then, is directly indecomposable if and only if and are the only idempotents in .
In the case when (assumed unital), the endomorphism ring , where each endomorphism arises as left multiplication by a fixed ring element. With this modification of notation, as right modules if and only if there exists a unique idempotent such that and . Thus every direct summand of is generated by an idempotent.
If is a central idempotent, then the corner ring is a ring with multiplicative identity . Just as idempotents determine the direct decompositions of as a module, the central idempotents of determine the decompositions of as a direct sum of rings. If is the direct sum of the rings , ..., , then the identity elements of the rings are central idempotents in , pairwise orthogonal, and their sum is . Conversely, given central idempotents , ..., in that are pairwise orthogonal and have sum , then is the direct sum of the rings , ..., . So in particular, every central idempotent in gives rise to a decomposition of as a direct sum of the corner rings and . As a result, a ring is directly indecomposable as a ring if and only if the identity is centrally primitive.
Working inductively, one can attempt to decompose into a sum of centrally primitive elements. If is centrally primitive, we are done. If not, it is a sum of central orthogonal idempotents, which in turn are primitive or sums of more central idempotents, and so on. The problem that may occur is that this may continue without end, producing an infinite family of central orthogonal idempotents. The condition " does not contain infinite sets of central orthogonal idempotents" is a type of finiteness condition on the ring. It can be achieved in many ways, such as requiring the ring to be right Noetherian. If a decomposition exists with each a centrally primitive idempotent, then is a direct sum of the corner rings , each of which is ring irreducible.
For associative algebras or Jordan algebras over a field, the Peirce decomposition is a decomposition of an algebra as a sum of eigenspaces of commuting idempotent elements.
Relation with involutions
If is an idempotent of the endomorphism ring , then the endomorphism is an -module involution of . That is, is an -module homomorphism such that is the identity endomorphism of .
An idempotent element of and its associated involution gives rise to two involutions of the module , depending on viewing as a left or right module. If represents an arbitrary element of , can be viewed as a right -module homomorphism so that , or can also be viewed as a left -module homomorphism , where .
This process can be reversed if is an invertible element of : if is an involution, then and are orthogonal idempotents, corresponding to and . Thus for a ring in which is invertible, the idempotent elements correspond to involutions in a one-to-one manner.
Category of R-modules
Lifting idempotents also has major consequences for the category of -modules. All idempotents lift modulo if and only if every direct summand of has a projective cover as an -module. Idempotents always lift modulo nil ideals and rings for which is -adically complete.
Lifting is most important when , the Jacobson radical of . Yet another characterization of semiperfect rings is that they are semilocal rings whose idempotents lift modulo .
Lattice of idempotents
One may define a partial order on the idempotents of a ring as follows: if and are idempotents, we write if and only if . With respect to this order, is the smallest and the largest idempotent. For orthogonal idempotents and , is also idempotent, and we have and . The atoms of this partial order are precisely the primitive idempotents.
When the above partial order is restricted to the central idempotents of , a lattice structure, or even a Boolean algebra structure, can be given. For two central idempotents and , the complement is given by
,
the meet is given by
.
and the join is given by
The ordering now becomes simply if and only if , and the join and meet satisfy and . It is shown in that if is von Neumann regular and right self-injective, then the lattice is a complete lattice.
Notes
Citations
References
idempotent at FOLDOC
Ring theory | Idempotent (ring theory) | [
"Mathematics"
] | 2,451 | [
"Fields of abstract algebra",
"Ring theory"
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361,969 | https://en.wikipedia.org/wiki/Radium%20chloride | Radium chloride is an inorganic compound with the chemical formula . It is a radium salt of hydrogen chloride. It was the first radium compound isolated in a pure state. Marie Curie and André-Louis Debierne used it in their original separation of radium from barium. The first preparation of radium metal was by the electrolysis of a solution of this salt using a mercury cathode.
Preparation
Radium chloride crystallises from aqueous solution as the dihydrate. The dihydrate is dehydrated by heating to 100 °C in air for one hour followed by 5.5 hours at 520 °C under argon. If the presence of other anions is suspected, the dehydration may be effectuated by fusion under hydrogen chloride.
Radium chloride can also be prepared by heating radium bromide in a flow of dry hydrogen chloride gas. It can be produced by treating radium carbonate with hydrochloric acid.
Properties
Radium chloride is a colorless salt with a blue-green luminescence, especially when heated. Its color gradually changes to yellow with aging, whereas contamination by barium may impart a rose tint. It is less soluble in water than other alkaline earth metal chlorides – at 25 °C its solubility is 245 g/L whereas that of barium chloride is 307 g/L, and the difference is even larger in hydrochloric acid solutions. This property is used in the first stages of the separation of radium from barium by fractional crystallization. Radium chloride is only sparingly soluble in azeotropic hydrochloric acid and virtually insoluble in concentrated hydrochloric acid.
Gaseous shows strong absorptions in the visible spectrum at 676.3 nm and 649.8 nm (red): the dissociation energy of the radium–chlorine bond is estimated as 2.9 eV, and its length as 292 pm.
Contrary to diamagnetic barium chloride, radium chloride is weakly paramagnetic with a magnetic susceptibility of 1.05. Its flame color is red.
Uses
Radium chloride is still used for the initial stages of the separation of radium from barium during the extraction of radium from pitchblende. The large quantities of material involved (to extract a gram of pure radium metal, about 7 tonnes of pitchblende is required) favour this less costly (but less efficient) method over those based on radium bromide or radium chromate (used for the later stages of the separation).
It was also used in medicine to produce radon gas which in turn was used as a brachytheraputic cancer treatment.
Radium-223 dichloride (USP, radium chloride Ra 223), tradename Xofigo (formerly Alpharadin), is an alpha-emitting radiopharmaceutical. Bayer received FDA approval for this drug to treat prostate cancer osteoblastic bone metastases in May 2013. Radium-223 chloride is one of the most potent ((antineoplastic drugs)) known. One dose (50 kBq/kg) in an adult is about 60 nanograms; this amount is 1/1000 the weight of an eyelash (75 micrograms).
References
Bibliography
Gmelins Handbuch der anorganischen Chemie (8. Aufl.), Berlin:Verlag Chemie, 1928, pp. 60–61.
Chlorides
Alkaline earth metal halides
Radium compounds | Radium chloride | [
"Chemistry"
] | 742 | [
"Chlorides",
"Inorganic compounds",
"Salts"
] |
362,025 | https://en.wikipedia.org/wiki/Active%20noise%20control | Active noise control (ANC), also known as noise cancellation (NC), or active noise reduction (ANR), is a method for reducing unwanted sound by the addition of a second sound specifically designed to cancel the first. The concept was first developed in the late 1930s; later developmental work that began in the 1950s eventually resulted in commercial airline headsets with the technology becoming available in the late 1980s. The technology is also used in road vehicles, mobile telephones, earbuds, and headphones.
Explanation
Sound is a pressure wave, which consists of alternating periods of compression and rarefaction. A noise-cancellation speaker emits a sound wave with the same amplitude but with an inverted phase (also known as antiphase) relative to the original sound. The waves combine to form a new wave, in a process called interference, and effectively cancel each other out – an effect which is called destructive interference.
Modern active noise control is generally achieved through the use of analog circuits or digital signal processing. Adaptive algorithms are designed to analyze the waveform of the background aural or nonaural noise, then based on the specific algorithm generate a signal that will either phase shift or invert the polarity of the original signal. This inverted signal (in antiphase) is then amplified and a transducer creates a sound wave directly proportional to the amplitude of the original waveform, creating destructive interference. This effectively reduces the volume of the perceivable noise.
A noise-cancellation speaker may be co-located with the sound source to be attenuated. In this case, it must have the same audio power level as the source of the unwanted sound in order to cancel the noise. Alternatively, the transducer emitting the cancellation signal may be located at the location where sound attenuation is wanted (e.g. the user's ear). This requires a much lower power level for cancellation but is effective only for a single user. Noise cancellation at other locations is more difficult as the three-dimensional wavefronts of the unwanted sound and the cancellation signal could match and create alternating zones of constructive and destructive interference, reducing noise in some spots while doubling noise in others. In small enclosed spaces (e.g. the passenger compartment of a car) global noise reduction can be achieved via multiple speakers and feedback microphones, and measurement of the modal responses of the enclosure.
Applications
Applications can be 1-dimensional or 3-dimensional, depending on the type of zone to protect. Periodic sounds, even complex ones, are easier to cancel than random sounds due to the repetition in the waveform.
Protection of a 1-dimension zone is easier and requires only one or two microphones and speakers to be effective. Several commercial applications have been successful: noise-canceling headphones, active mufflers, anti-snoring devices, vocal or center channel extraction for karaoke machines, and the control of noise in air conditioning ducts. The term 1-dimension refers to a simple pistonic relationship between the noise and the active speaker (mechanical noise reduction) or between the active speaker and the listener (headphones).
Protection of a 3-dimensional zone requires many microphones and speakers, making it more expensive. Noise reduction is more easily achieved with a single listener remaining stationary but if there are multiple listeners or if the single listener turns their head or moves throughout the space then the noise reduction challenge is made much more difficult. High-frequency waves are difficult to reduce in three dimensions due to their relatively short audio wavelength in air. The wavelength in air of sinusoidal noise at approximately 800 Hz is double the distance of the average person's left ear to the right ear; such a noise coming directly from the front will be easily reduced by an active system but coming from the side will tend to cancel at one ear while being reinforced at the other, making the noise louder, not softer. High-frequency sounds above 1000 Hz tend to cancel and reinforce unpredictably from many directions. In sum, the most effective noise reduction in three-dimensional space involves low-frequency sounds. Commercial applications of 3-D noise reduction include the protection of aircraft cabins and car interiors, but in these situations, protection is mainly limited to the cancellation of repetitive (or periodic) noise such as engine-, propeller- or rotor-induced noise. This is because an engine's cyclic nature makes analysis and noise cancellation easier to apply.
Modern mobile phones use a multi-microphone design to cancel out ambient noise from the speech signal. Sound is captured from the microphone(s) furthest from the mouth (the noise signal(s)) and from the one closest to the mouth (the desired signal). The signals are processed to cancel the noise from the desired signal, producing improved voice sound quality.
In some cases, noise can be controlled by employing active vibration control. This approach is appropriate when the vibration of a structure produces unwanted noise by coupling the vibration into the surrounding air or water.
Active vis-à-vis passive noise control
Noise control is an active or passive means of reducing sound emissions, often for personal comfort, environmental considerations, or legal compliance. Active noise control is sound reduction using a power source. Passive noise control is sound reduction by noise-isolating materials such as insulation, sound-absorbing tiles, or a muffler rather than a power source.
Active noise canceling is best suited for low frequencies. For higher frequencies, the spacing requirements for free space and zone of silence techniques become prohibitive. In acoustic cavity and duct-based systems, the number of nodes grows rapidly with increasing frequency, which quickly makes active noise control techniques unmanageable. Passive treatments become more effective at higher frequencies and often provide an adequate solution without the need for active control.
History
The first patent for a noise control system——was granted to inventor Paul Lueg in 1936. The patent described how to cancel sinusoidal tones in ducts by phase-advancing the wave and canceling arbitrary sounds in the region around a loudspeaker by inverting the polarity. In the 1950s Lawrence J. Fogel patented systems to cancel the noise in helicopter and airplane cockpits. In 1957 Willard Meeker developed a working model of active noise control applied to a circumaural earmuff. This headset had an active attenuation bandwidth of approximately 50–500 Hz, with a maximum attenuation of approximately 20 dB. By the late 1980s the first commercially available active noise reduction headsets became available. They could be powered by NiCad batteries or directly from the aircraft power system.
See also
Active sound design
Adaptive noise cancelling
Coherence (physics)
Noise-canceling microphone
Notes
References
External links
BYU physicists quiet fans in computers, office equipment
Anti-Noise, Quieting the Environment with Active Noise Cancellation Technology, IEEE Potentials, April 1992
Christopher E. Ruckman's ANC FAQ (This page was created in 1994 and maintained until approximately 2010, but is no longer active.)
Waves of Silence: Digisonix, active noise control, and the digital revolution
Audio engineering
Noise reduction
Noise control
Loudspeaker technology | Active noise control | [
"Engineering"
] | 1,451 | [
"Electrical engineering",
"Audio engineering"
] |
362,070 | https://en.wikipedia.org/wiki/Ignition%20system | Ignition systems are used by heat engines to initiate combustion by igniting the fuel-air mixture. In a spark ignition versions of the internal combustion engine (such as petrol engines), the ignition system creates a spark to ignite the fuel-air mixture just before each combustion stroke. Gas turbine engines and rocket engines normally use an ignition system only during start-up.
Diesel engines use compression ignition to ignite the fuel-air mixture using the heat of compression and therefore do not use an ignition system. They usually have glowplugs that preheat the combustion chamber to aid starting in cold weather.
Early cars used ignition magneto and trembler coil systems, which were superseded by Distributor-based systems (first used in 1912). Electronic ignition systems (first used in 1968) became common towards the end of the 20th century, with coil-on-plug versions of these systems becoming widespread since the 1990s.
Magneto and mechanical systems
Ignition magneto systems
An ignition magneto (also called a high-tension magneto) is an older type of ignition system used in spark-ignition engines (such as petrol engines). It uses a magneto and a transformer to make pulses of high voltage for the spark plugs. The older term "high-tension" means "high-voltage".
Used on many cars in the early 20th century, ignition magnetos were largely replaced by induction coil ignition systems. The use of ignition magnetos is now confined mainly to engines without a battery, for example in lawnmowers and chainsaws. It is also used in modern piston-engined aircraft (even though a battery is present), to avoid the engine relying on an electrical system.
Induction coil systems
As batteries became more common in cars (due to the increased usage of electric starter motors), magneto systems were replaced by systems using an induction coil. The 1886 Benz Patent-Motorwagen and the 1908 Ford Model T used a trembler coil ignition system, whereby the trembler interrupted the current through the coil and caused a rapid series of sparks during each firing. The trembler coil would be energized at an appropriate point in the engine cycle. In the Model T, the four-cylinder engine had a trembler coil for each cylinder.
Distributor-based systems
An improved ignition system was invented by Charles Kettering at Delco in the United States and introduced in Cadillac's 1912 cars. The Kettering ignition system consisted of a single ignition coil, breaker points, a capacitor (to prevent the points from arcing at break) and a distributor (to direct the electricity from the ignition coil to the correct cylinder). The Kettering system became the primary ignition system for many years in the automotive industry due to its lower cost and relative simplicity.
Electronic systems
The first electronic ignition (a cold cathode type) was tested in 1948 by Delco-Remy, while Lucas introduced a transistorized ignition in 1955, which was used on BRM and Coventry Climax Formula One engines in 1962. The aftermarket began offering EI that year, with both the AutoLite Electric Transistor 201 and Tung-Sol EI-4 (thyratron capacitive discharge) being available. Pontiac became the first automaker to offer an optional EI, the breakerless magnetic pulse-triggered Delcotronic, on some 1963 models; it was also available on some Corvettes. The first commercially available all solid-state (SCR) capacitive discharge ignition was manufactured by Hyland Electronics in Canada also in 1963. Ford fitted a FORD designed breakerless system on the Lotus 25s entered at Indianapolis the next year, ran a fleet test in 1964, and began offering optional EI on some models in 1965. This electronic system was utilized on the GT40s campaigned by Shelby American and Holman and Moody. Robert C. Hogle, Ford Motor Company, presented the, "Mark II-GT Ignition and Electrical System", Publication #670068, at the SAE Congress, Detroit, Michigan, January 9–13, 1967. Beginning in 1958, Earl W. Meyer at Chrysler worked on EI, continuing until 1961 and resulting in use of EI on the company's NASCAR hemis in 1963 and 1964.
Prest-O-Lite's CD-65, which relied on capacitance discharge (CD), appeared in 1965, and had "an unprecedented 50,000 mile warranty." (This differs from the non-CD Prest-O-Lite system introduced on AMC products in 1972, and made standard equipment for the 1975 model year.) A similar CD unit was available from Delco in 1966, which was optional on Oldsmobile, Pontiac, and GMC vehicles in the 1967 model year. Also in 1967, Motorola debuted their breakerless CD system. The most famous aftermarket electronic ignition which debuted in 1965, was the Delta Mark 10 capacitive discharge ignition, which was sold assembled or as a kit.
The Fiat Dino was the first production car to come standard with EI in 1968, followed by the Jaguar XJ Series 1 in 1971, Chrysler (after a 1971 trial) in 1973 and by Ford and GM in 1975.
In 1967, Prest-O-Lite made a "Black Box" ignition amplifier, intended to take the load off the distributor's breaker points during high rpm runs, which was used by Dodge and Plymouth on their factory Super Stock Coronet and Belvedere drag racers. This amplifier was installed on the interior side of the cars' firewall, and had a duct which provided outside air to cool the unit. The rest of the system (distributor and spark plugs) remains as for the mechanical system. The lack of moving parts compared with the mechanical system leads to greater reliability and longer service intervals.
A variation coil-on-plug ignition has each coil handle two plugs, on cylinders which are 360 degrees out of phase (and therefore reach top dead center (TDC) at the same time); in the four-cycle engine this means that one plug will be sparking during the end of the exhaust stroke while the other fires at the usual time, a so-called "wasted spark" arrangement which has no drawbacks apart from faster spark plug erosion; the paired cylinders are 1/4 and 2/3 on four cylinder arrangements, 1/4, 6/3, 2/5 on six cylinder engines and 6/7, 4/1, 8/3 and 2/5 on V8 engines. Other systems do away with the distributor as a timing apparatus and use a magnetic crank angle sensor mounted on the crankshaft to trigger the ignition at the proper time.
Engine Control Units
Modern automotive engines use an engine control unit (ECU), which is a single device that controls various engine functions including the ignition system and the fuel injection. This contrasts earlier engines, where the fuel injection and ignition were operated as separate systems.
Gas turbine and rocket engines
Gas turbine engines (including jet engines) use capacitor discharge ignition, however the ignition system is only used at startup or when the combustor(s) flame goes out.
The ignition system in a rocket engine is critical to avoiding a hard start or explosion. Rockets often employ pyrotechnic devices that place flames across the face of the injector plate, or, alternatively, hypergolic propellants that ignite spontaneously on contact with each other.
See also
Electromagnetism
Faraday's law of induction
History of the internal combustion engine
References
Auto parts
Applications of control engineering
Engine components | Ignition system | [
"Technology",
"Engineering"
] | 1,543 | [
"Engine components",
"Control engineering",
"Engines",
"Applications of control engineering"
] |
362,089 | https://en.wikipedia.org/wiki/Matthew%20Fontaine%20Maury | Matthew Fontaine Maury (January 14, 1806February 1, 1873) was an American oceanographer and naval officer, serving the United States and then joining the Confederacy during the American Civil War.
He was nicknamed "Pathfinder of the Seas" and is considered a founder of modern oceanography. He wrote extensively on the subject, and his book, The Physical Geography of the Sea (1855), was the first comprehensive work on oceanography to be published.
In 1825, at 19, Maury obtained, through U.S. Representative Sam Houston, a midshipman's warrant in the United States Navy. As a midshipman on board the frigate , he almost immediately began to study the seas and record methods of navigation. When a leg injury left him unfit for sea duty, Maury devoted his time to studying navigation, meteorology, winds, and currents.
He became Superintendent of the Depot of Charts and Instruments, later renamed the United States Naval Observatory, in 1844. There, Maury studied thousands of ships' logs and charts. He published the Wind and Current Chart of the North Atlantic, which showed sailors how to use the ocean's currents and winds to their advantage, drastically reducing the length of ocean voyages. Maury's uniform system of recording oceanographic data was adopted by navies and merchant marines worldwide and was used to develop charts for all the major trade routes.
With the outbreak of the American Civil War, Maury, a Virginian, resigned his commission as a U.S. Navy commander and joined the Confederacy. He spent the war in the Southern United States, and Great Britain and France as a Confederate envoy. He helped the Confederacy acquire a ship, , while trying to convince several European powers to help stop the war. Following the war, Maury was eventually pardoned; he accepted a teaching position at the Virginia Military Institute in Lexington, Virginia.
He died at the institute in 1873 after he had completed an exhausting state-to-state lecture tour on national and international weather forecasting on land. He had also completed his book, Geological Survey of Virginia, and a new series on geography for young people.
Early life and career
Maury was a descendant of the Maury family, a prominent Virginia family of Huguenot ancestry that can be traced back to 15th-century France. His grandfather (the Reverend James Maury) was an inspiring teacher to a future U.S. president, Thomas Jefferson. Maury also had Dutch-American ancestry from the Minor family of early Virginia.
He was born in 1806 in Spotsylvania County, Virginia, near Fredericksburg; his parents were Richard Maury and Diane Minor Maury. The family moved to Franklin, Tennessee when he was five. He wanted to emulate the naval career of his older brother, Flag Lieutenant John Minor Maury, an officer in the U.S. Navy, who caught yellow fever after fighting pirates. As a result of John's painful death, Matthew's father, Richard, forbade him from joining the Navy. Maury strongly considered attending West Point to get a better education than the Navy could offer. Instead, he obtained a naval appointment through the influence of Tennessee Representative Sam Houston, a family friend, in 1825, at the age of 19.
Maury joined the Navy as a midshipman on board the frigate , which was carrying the elderly Marquis de La Fayette home to France following his famous 1824 visit to the United States. Almost immediately, Maury began to study the seas and to record methods of navigation. One of the experiences that piqued this interest was circumnavigating the globe on the , his assigned ship and the first U.S. warship to travel around the world.
Scientific career
Maury's seagoing days ended abruptly at the age of 33 after he broke his right leg in a stagecoach accident. After that he studied naval meteorology, navigation, and charting the winds and currents. He told his family that his work was inspired by Psalm 8, "Thou madest him to have dominion over the works of thy hands... and whatsoever passeth through the paths of the seas."
As officer-in-charge of the United States Navy office in Washington, DC, called the "Depot of Charts and Instruments," the young lieutenant became a librarian of the many unorganized log books and records in 1842. On his initiative, he sought to improve seamanship by organizing the information in his office and instituting a reporting system among the nation's shipmasters to gather further information on sea conditions and observations. The product of his work was international recognition and the publication in 1847 of Wind and Current Chart of the North Atlantic, causing the change of purpose and renaming of the depot to the United States Naval Observatory and Hydrographical Office in 1854. He held that position until his resignation in April 1861. Maury was one of the principal advocates for founding a national observatory and he appealed to a science enthusiast and former U.S. president, Representative John Quincy Adams, for the creation of what would eventually become the Naval Observatory. Maury occasionally hosted Adams, who enjoyed astronomy as an avocation, at the Naval Observatory. Concerned that Maury always had a long trek to and from his home on upper Pennsylvania Avenue, Adams introduced an appropriations bill that funded a Superintendent's House on the Observatory grounds. Adams thus felt no constraint in regularly stopping by for a look through the facility's telescope.
As a sailor, Maury noted numerous lessons that ship masters had learned about the effects of adverse winds and drift currents on the path of a ship. The captains recorded the lessons faithfully in their logbooks, which were then forgotten. At the Observatory, Maury uncovered an enormous collection of thousands of old ships' logs and charts in storage in trunks dating back to the start of the U.S. Navy. He pored over the documents, collecting information on winds, calms, and currents for all seas in all seasons. His dream was to put that information in the hands of all captains.
Maury's work on ocean currents and investigations of the whaling industry led him to suspect that a warm-water, ice-free northern passage existed between the Atlantic and Pacific. He thought he detected a warm surface current pushing into the Arctic, and logs of old whaling ships indicated that whales killed in the Atlantic bore harpoons from ships in the Pacific (and vice versa). The frequency of these occurrences seemed unlikely if the whales had traveled around Cape Horn.
Lieutenant Maury published his Wind and Current Chart of the North Atlantic, which showed sailors how to use the ocean's currents and winds to their advantage, drastically reducing the length of voyages. His Sailing Directions and Physical Geography of the Seas and Its Meteorology remain standard. Maury's uniform system of recording synoptic oceanographic data was adopted by navies and merchant marines around the world and was used to develop charts for all the major trade routes.
Maury's Naval Observatory team included midshipmen assigned to him: James Melville Gilliss, Lieutenants John Mercer Brooke, William Lewis Herndon, Lardner Gibbon, Isaac Strain, John "Jack" Minor Maury II of the USN 1854 Darien Exploration Expedition, and others. Their duty at the observatory was always temporary, and new men had to be trained repeatedly. Thus Lt. Maury was simultaneously employed with astronomical and nautical work, as well as constantly training new temporary men to assist in these works. As his reputation grew, the competition among young midshipmen to be assigned to work with him intensified. Thus, he always had able assistants.
Maury advocated for naval reform, including a school for the Navy that would rival the Army's United States Military Academy. That reform was heavily pushed by Maury's "Scraps from the Lucky Bag" and other articles printed in the newspapers, bringing about many changes in the Navy, including his finally fulfilled dream of the creation of the United States Naval Academy.
During its first 1848 meeting, he helped launch the American Association for the Advancement of Science (AAAS).
In 1849, Maury spoke out on the need for a transcontinental railroad to join the Eastern United States to California. He recommended a southerly route with Memphis, Tennessee, as the eastern terminus, as it is equidistant from Lake Michigan and the Gulf of Mexico. He argued that a southerly route running through Texas would avoid winter snows and could open up commerce with the northern states of Mexico. Maury also advocated construction of a railroad across the Isthmus of Panama.
For his scientific endeavors, Maury was elected to the American Philosophical Society in 1852.
International meteorological conference
Maury also called for an international sea and land weather service. Having charted the seas and currents, he worked on charting land weather forecasting. Congress refused to appropriate funds for a land system of weather observations.
Maury became convinced that adequate scientific knowledge of the sea could be obtained only through international cooperation. He proposed that the United States invite the maritime nations of the world to a conference to establish a "universal system" of meteorology, and he was the leading spirit of a pioneer scientific conference when it met in Brussels in 1853. Within a few years, nations owning three-fourths of the shipping of the world were sending their oceanographic observations to Maury at the Naval Observatory, where the information was evaluated and the results were given worldwide distribution.
As its representative at the conference, the United States sent Maury. As a result of the Brussels Conference, many nations, including many traditional enemies, agreed to cooperate in sharing land and sea weather data using uniform standards. It was soon after the Brussels conference that Prussia, Spain, Sardinia, the Free City of Hamburg, the Republic of Bremen, Chile, Austria, Brazil, and others agreed to join the enterprise.
The Pope established honorary flags of distinction for the ships of the Papal States, which could be awarded only to the vessels that filled out and sent to Maury in Washington, DC, the Maury abstract logs.
Proposed deportation of slaves to Brazil
Maury's stance on the institution of slavery has been termed "proslavery international". Maury, along with other politicians, newspaper editors, merchants, and United States government officials, envisioned a future for slavery that linked the United States, the Caribbean Sea, and the Amazon basin in Brazil. He believed the future of United States commerce lay in South America, colonized by white southerners and their enslaved people. There, Maury claimed, was "work to be done by Africans with the American axe in his hand." In the 1850s, he studied a way to send Virginia's slaves to Brazil as a way to phase out slavery in the state gradually. Maury was aware of an 1853 survey of the Amazon region conducted by the Navy Lt. William Lewis Herndon. The 1853 expedition aimed to map the area for trade so that American traders could go "with their goods and chattels [including enslaved people] to settle and to trade goods from South American countries along the river highways of the Amazon valley". Brazil maintained legal enslavement but had prohibited the importation of newly enslaved people from Africa in 1850 under the pressure of the British. Maury proposed that moving people enslaved in the United States to Brazil would reduce or eliminate slavery over time in as many areas of the southern United States as possible and would end new enslavement for Brazil. Maury's primary concern, however, was neither the freedom of enslaved people nor the amelioration of slavery in Brazil, but rather an absolution for slaveholders of Virginia and other southern states. Maury wrote to his cousin, "Therefore I see in the slave territory of the Amazon the SAFETY VALVE of the Southern States."
Maury wanted to open up the Amazon to free navigation in his plan. However, Emperor Pedro II's government firmly rejected the proposals, and Maury's proposal received little or no support in the United States, especially in the South, which sought to perpetuate the institution and the riches made off the yoke of slavery. By 1855, the proposal had failed. Brazil authorized free navigation to all nations in the Amazon in 1866, only when it was at war against Paraguay, when free navigation in the area had become necessary.
Maury was not an enslaver, but he did not actively oppose the institution of slavery. An article tying his legacy in oceanography to the slave trade suggested that Maury was ambivalent about slavery, seeing it as wrong but not intent on forcing others to free enslaved people. However, a recent article explaining the removal of his monument from Monument Avenue in Richmond, Virginia, illustrated a proslavery stance through deep ties to the slave trade that accompanied his scientific achievements.
American Civil War
Maury staunchly opposed secession, but in 1860, he wrote letters to the governors of New Jersey, Pennsylvania, Delaware, and Maryland urging them to stop the momentum toward war. When Virginia declared secession in April 1861, Maury nonetheless resigned his commission in the U.S. Navy, choosing to fight against the North. With the outbreak of the American Civil War, Maury joined the Confederacy.
Upon his resignation from the U.S. Navy, the Virginia governor appointed Maury commander of the Virginia Navy. When this was consolidated into the Confederate Navy, Maury was made a Commander in the Confederate States Navy and appointed as chief of the Naval Bureau of Coast, Harbor, and River Defense. In this role, Maury helped develop the first electrically controlled naval mine, which caused havoc for U.S. shipping. He'd had experience with transatlantic cable and electricity flowing through wires underwater when working with Cyrus West Field and Samuel Finley Breese Morse. The naval mines, called torpedoes at that time, were similar to present-day contact mines and were said by the Secretary of the Navy in 1865 "to have cost the Union more vessels than all other causes combined."
In September 1862, Maury, partly because of his international reputation, and partly due to jealousy of superior officers who wanted him placed at some distance, was ordered on special service to England. There, he sought to purchase and fit ships for the Confederacy and persuade European powers to recognize and support the Confederacy. Maury traveled to England, Ireland, and France, acquiring and fitting out ships for the Confederacy and soliciting supplies. Through speeches and newspaper publications, Maury unsuccessfully called for European nations to intercede on behalf of the Confederacy and help end the American Civil War. Maury established relations for the Confederacy with Emperor Napoleon III of France and Archduke Maximilian of Austria, who, on April 10, 1864, was proclaimed Emperor of Mexico.
At an early stage in the war, the Confederate States Congress assigned Maury and Francis H. Smith, a mathematics professor at the University of Virginia, to develop a system of weights and measures.
Later life
Maury was in the West Indies on his way back to the Confederacy when he learned of its collapse. The war had brought ruin to many in Fredericksburg, where Maury's immediate family lived. On the advice of Robert E. Lee and other friends, he decided not to return to Virginia but sent a letter of surrender to U.S. naval forces in the Gulf of Mexico and headed for Mexico. There Maximilian, whom he had met in Europe, appointed him "Imperial Commissioner of Colonization". Maury and Maximilian planned to entice former Confederates to emigrate to Mexico, building Carlotta and New Virginia Colony for displaced Confederates and immigrants from other lands. Upon learning of the plan, Lee wrote Maury saying, "The thought of abandoning the country, and all that must be left in it, is abhorrent to my feelings, and I prefer to struggle for its restoration, and share its fate, rather than to give up all as lost." In the end, the plan did not attract the intended immigrants and Maximilian, facing increasing opposition in Mexico, ended it. Maury then returned to England in 1866 and found work there.
In 1868 he was pardoned by the federal government and returned to the US, accepting a teaching position at the Virginia Military Institute in Lexington, Virginia, holding the chair of physics. While in Lexington, he completed a physical survey of Virginia, which he documented in the book The Physical Geography of Virginia. He had once been a gold mining superintendent outside Fredericksburg and had studied geology intensely during that time, so he was well-equipped to write such a book. He aimed to assist war-torn Virginia in rebuilding by discovering and extracting minerals, improving farming, etc. He lectured extensively in the United States and abroad. He advocated for creating a state agricultural college as an adjunct to Virginia Military Institute. This led to the establishment at Blacksburg of the Virginia Agricultural and Mechanical College, later renamed Virginia Polytechnic Institute and State University, in 1872. Maury was offered the position as its first president but turned it down because of his age.
He had previously been suggested as president of the College of William & Mary in Williamsburg, Virginia, in 1848 by Benjamin Blake Minor in his publication the Southern Literary Messenger. He considered becoming president of St. John's College in Annapolis, Maryland, the University of Alabama, and the University of Tennessee. From statements that he made in letters, it appears that he preferred being close to General Robert E. Lee in Lexington, where Lee was president of Washington College. Maury served as a pallbearer for Lee. He also gave talks in Europe about cooperation on a weather bureau for land, just as he had charted the winds and predicted storms at sea many years before. He gave speeches until his last days when he collapsed while giving one. He went home after he recovered and told his wife Ann Hull Herndon-Maury, "I have come home to die."
Death and burial
He died at home in Lexington at 12:40 pm on Saturday, February 1, 1873. He was exhausted from traveling throughout the nation giving speeches promoting land meteorology. His eldest son, Major Richard Launcelot Maury, and son-in-law, Major Spottswood Wellford Corbin, attended him at the time. Maury asked his daughters and wife to leave the room. His last words, recorded verbatim, were "all's well," a nautical expression meaning calm conditions at sea.
His body was placed on display in the Virginia Military Institute library. Maury was initially buried in the Gilham family vault in Lexington's cemetery, across from Stonewall Jackson, until, after some delay, his remains were taken through Goshen Pass to Richmond, Virginia the following year He was reburied between Presidents James Monroe and John Tyler in Hollywood Cemetery in Richmond, Virginia.
Legacy
After decades of national and international work, Maury received fame and honors, including being knighted by several nations and given medals with precious gems as well as a collection of all medals struck by Pope Pius IX during his pontificate, a book dedication and more from Father Angelo Secchi, who was a student of Maury from 1848 to 1849 in the United States Naval Observatory. The two remained lifelong friends. Other religious friends of Maury included James Hervey Otey, his former teacher who, before 1857, worked with Bishop Leonidas Polk on the construction of the University of the South in Tennessee. While visiting there, Maury was convinced by his old teacher to give the "cornerstone speech."
As a U.S. Navy officer, he was required to decline awards from foreign nations. Some were offered to Maury's wife, Ann Hull Herndon-Maury, who accepted them for her husband. Some have been placed at Virginia Military Institute or lent to the Smithsonian. He became a commodore (often a title of courtesy) in the Virginia Provisional Navy and a Commander in the Confederacy.
Buildings on several college campuses are named in his honor. Maury Hall was the home of the Naval Science Department at the University of Virginia and headquarters of the university's Navy ROTC battalion until being renamed in 2022. The original building of the College of William & Mary Virginia Institute of Marine Science is named Maury Hall as well. Another Maury Hall housed the Electrical and Computer Engineering Department and the Robotics and Control Engineering Department at the United States Naval Academy in Annapolis, Maryland. On February 17, 2023, the academy announced that it had renamed this building in honor of Jimmy Carter, the only Naval Academy graduate to become President of the United States. The change had been recommended by a naming commission created by federal law to reexamine Confederate-related names and symbols on military installations. James Madison University also has a Maury Hall, the university's first academic and administrative building. In the wake of the 2020 George Floyd protests, JMU student organizations called for renaming the building. On Monday, June 22, 2020, hearing the calls of students and alums, the university president announced it would recommend to the JMU board of visitors to rename Maury Hall, along with Ashby Hall and Jackson Hall.
Ships have been named in his honor, including various vessels named ; USS Commodore Maury (SP-656), a patrol vessel and minesweeper of World War I; and a World War II Liberty Ship. Additionally, Tidewater Community College, based in Norfolk, Virginia, owns the R/V Matthew F. Maury. The ship is used for oceanography research and student cruises. In March 2013, the U.S. Navy launched the oceanographic survey ship USNS Maury (T-AGS-66), in 2023 the ship was renamed USNS Marie Tharp.
The Mariners' Lake, in Newport News, Virginia, had been named after Maury but had its name changed during the George Floyd protests. The lake is located on the Mariners' Museum property and is encircled by a walking trail.
The Maury River, entirely in Rockbridge County, Virginia, near Virginia Military Institute (where Maury taught), also honors the scientist, as does Maury crater, on the Moon.
Matthew Fontaine Maury High School in Norfolk, Virginia, is named after him. Matthew Maury Elementary School in Alexandria, Virginia, was built in 1929. Nearby Arlington, Va., renamed its 1910 Clarendon Elementary to honor Maury in 1944; Since 1976, the building has been home to the Arlington Arts Center (rebranded in 2022 as the Museum of Contemporary Art Arlington). There is a county historical marker outside the former school. Matthew Fontaine Maury School in Fredericksburg was built in 1919-1920 and closed in 1980. The building was converted into condominiums and is on the National Register of Historic Places. Adjoining it is Maury Stadium, built in 1935 and still used for local high school sports events.
Numerous historical markers commemorate Maury throughout the South, including those in Richmond, Virginia, Fletcher, North Carolina, Franklin, Tennessee, and several in Chancellorsville, Virginia.
The Matthew Fontaine Maury Papers collection at the Library of Congress contains over 14,000 items. It documents Maury's extensive career and scientific endeavors, including correspondence, notebooks, lectures, and written speeches.
On July 2, 2020, the mayor of Richmond, Levar Stoney ordered the removal of a statue of Maury erected in 1929 on Richmond's Monument Avenue. The mayor used his emergency powers to bypass a state-mandated review process, calling the statue a "severe, immediate and growing threat to public safety."
Publications
On the Navigation of Cape Horn
Whaling Charts
Wind and Current Charts
Explanations and Sailing Directions to Accompany the Wind and Current Charts, 1851, 1854, 1855
Lieut. Maury's Investigations of the Winds and Currents of the Sea, 1851
On the Probable Relation between Magnetism and the Circulation of the Atmosphere, 1851
Maury's Wind and Current Charts: Gales in the Atlantic, 1857
Observations to Determine the Solar Parallax, 1856
Amazon, and the Atlantic Slopes of South America, 1853
Commander M. F. Maury on American Affairs, 1861
The Physical Geography of the Sea and Its Meteorology, 1861
Maury's New Elements of Geography for Primary and Intermediate Classes
Geography: "First Lessons"
Elementary Geography: Designed for Primary and Intermediate Classes
Geography: "The World We Live In"
Published Address of Com. M. F. Maury, before the Fair of the Agricultural & Mechanical Society
Geology: A Physical Survey of Virginia; Her Geographical Position, Its Commercial Advantages and National Importance, Virginia Military Institute, 1869
See also
Bathymetric chart
Flying Cloud
National Institute for the Promotion of Science
Notable global oceanographers
Prophet Without Honor
References
Further reading
External links
. 1996 website retrieved via the Wayback Search Engine
CBNnews VIDEO on Commander Matthew Fontaine Maury "The Father of Modern Oceanography"
Naval Oceanographic Office—Matthew Fontaine Maury Oceanographic Library — The World's Largest Oceanographic Library.
United States Naval Sea Cadet Corps — Matthew Fontaine Maury — Pathfinders Division.
The Maury Project; A comprehensive national program of teacher enhancement based on studies of the physical foundations of oceanography.
The Mariner's Museum: Matthew Fontaine Maury Society.
Letter to President John Quincy Adams from Commander Matthew Fontaine Maury (1847) on the "National" United States Naval Observatory regarding a written description of the observatory, in detail, with other information relating thereto, including an explanation of the objects and uses of the various instruments.
The National (Naval) Observatory and The Virginia Historical Society (May 1849)
Biography of Matthew Fontaine Maury at U.S. Navy Historical Center.
The Diary of Betty Herndon Maury, daughter of Matthew Fontaine Maury, 1861–1863.
Matthew Fontaine Maury School in Richmond, Virginia, USA, 1950s. Photographer: Nina Leen. Approximately 200 TIME-LIFE photographs
Astronomical Observations from the Naval Observatory 1845.
Obituary in:
Sample charts by Maury held the American Geographical Society Library, UW Milwaukee in the digital map collection.
1806 births
1873 deaths
19th-century American astronomers
American earth scientists
19th-century American educators
19th-century American geographers
American oceanographers
American people of Dutch descent
American people of French descent
American Protestants
American science writers
Burials at Hollywood Cemetery (Richmond, Virginia)
Microscopists
People from Spotsylvania County, Virginia
People of Virginia in the American Civil War
Science and technology in the United States
United States Navy officers
Writers from Virginia
Hall of Fame for Great Americans inductees
Maury family (Virginia)
People from Franklin, Tennessee | Matthew Fontaine Maury | [
"Chemistry"
] | 5,379 | [
"Microscopists",
"Microscopy"
] |
362,116 | https://en.wikipedia.org/wiki/Robinson%20projection | The Robinson projection is a map projection of a world map that shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.
The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general-purpose world maps since that time. Robinson published details of the projection's construction in 1974. The National Geographic Society (NGS) began using the Robinson projection for general-purpose world maps in 1988, replacing the Van der Grinten projection. In 1998, NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles".
Strengths and weaknesses
The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt that this produced a better overall view than could be achieved by adhering to either. The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.
Hence, distortion close to the poles is severe, but quickly declines to moderate levels moving away from them. The straight parallels imply severe angular distortion at the high latitudes toward the outer edges of the map – a fault inherent in any pseudocylindrical projection. However, at the time it was developed, the projection effectively met Rand McNally's goal to produce appealing depictions of the entire world.
Formulation
The projection is defined by the table:
The table is indexed by latitude at 5-degree intervals; intermediate values are calculated using interpolation. Robinson did not specify any particular interpolation method, but it is reported that others used either Aitken interpolation (with polynomials of unknown degrees) or cubic splines while analyzing area deformation on the Robinson projection. The X column is the ratio of the length of the parallel to the length of the equator; the Y column can be multiplied by 0.2536 to obtain the ratio of the distance of that parallel from the equator to the length of the equator.
Coordinates of points on a map are computed as follows:
where R is the radius of the globe at the scale of the map, λ is the longitude of the point to plot, and λ0 is the central meridian chosen for the map (both λ and λ0 are expressed in radians).
Simple consequences of these formulas are:
With x computed as a constant multiplier to the meridian across the entire parallel, meridians of longitude are thus equally spaced along the parallel.
With y having no dependency on longitude, parallels are straight horizontal lines.
Applications
The Central Intelligence Agency World Factbook uses the Robinson projection in its political and physical world maps.
The European Centre for Disease Prevention and Control recommends using the Robinson projection for mapping the whole world.
See also
List of map projections
Cartography
Kavrayskiy VII
References
Further reading
Arthur H. Robinson (1974). "A New Map Projection: Its Development and Characteristics". In: International Yearbook of Cartography. Vol 14, 1974, pp. 145–155.
John B. Garver Jr. (1988). "New Perspective on the World". In: National Geographic, December 1988, pp. 911–913.
John P. Snyder (1993). Flattening The Earth—2000 Years of Map Projections, The University of Chicago Press. pp. 214–216.
External links
Table of examples and properties of all common projections, from radicalcartography.net
Numerical evaluation of the Robinson projection, from Cartography and Geographic Information Science, April, 2004 by Cengizhan Ipbuker
Map projections | Robinson projection | [
"Mathematics"
] | 758 | [
"Map projections",
"Coordinate systems"
] |
362,132 | https://en.wikipedia.org/wiki/Glans | The glans (, : glandes ; from the Latin word for "acorn") is a vascular structure located at the tip of the penis in male mammals or a homologous genital structure of the clitoris in female mammals.
Structure
The exterior structure of the glans consists of mucous membrane, which is usually covered by foreskin or clitoral hood in naturally developed genitalia. This covering, called the prepuce, is normally retractable in adulthood unless removed by circumcision.
The glans naturally joins with the frenulum of the penis or clitoris, as well as the inner labia in women, and the foreskin in men. In non-technical or sexual discussions, often the word "clitoris" refers to the external glans alone, excluding the clitoral hood, frenulum, and internal body of the clitoris. Similarly, phrases "tip" or "head" of the penis refers to the glans alone.
Sex differences in humans
In males, the glans is known as the glans penis, while in females the glans is known as the clitoral glans.
In females, the clitoris is above the urethra. The glans of the clitoris is the most highly innervated part of the external female genitalia.
In spotted hyenas, the female's pseudo-penis can be distinguished from the male's penis by its greater thickness and more rounded glans. In both male and female spotted hyenas, the base of the glans is covered with penile spines.
Development
In the development of the urinary and reproductive organs, the glans is derived from the genital tubercle.
See also
Glanuloplasty
References
Works cited
Sexual anatomy | Glans | [
"Biology"
] | 379 | [
"Behavior",
"Sex",
"Sexuality stubs",
"Sexual anatomy",
"Sexuality"
] |
362,138 | https://en.wikipedia.org/wiki/MetroCard | The MetroCard is a magnetic stripe card used for fare payment on transportation in the New York City area. It is a payment method for the New York City Subway (including the Staten Island Railway), New York City Transit buses and MTA buses. The MetroCard is also accepted by several partner agencies: Nassau Inter-County Express (NICE), the PATH train system, the Roosevelt Island Tramway, AirTrain JFK, and Westchester County's Bee-Line Bus System.
The MetroCard was introduced in 1993 to enhance the technology of the transit system and eliminate the burden of carrying and collecting tokens. The MTA discontinued the use of tokens in the subway on May 3, 2003, and on buses on December 31, 2003.
The MetroCard is expected to be phased out by 2025. It will be replaced by OMNY, a contactless payment system where riders pay for their fare by waving or tapping credit or debit bank cards, smartphones, or MTA-issued smart cards.
The MetroCard is managed by a division of the MTA known as Revenue Control, MetroCard Sales, which is part of the Office of the Executive Vice President. The MetroCard Vending Machines are manufactured by Cubic Transportation Systems, Inc.
As of early 2019, the direct costs of the MetroCard system had totaled $1.5 billion.
History and fares
The idea for a farecard with a magnetic strip for the MTA system was proposed in 1983. It was the "highest priority" for then-MTA Chairman Richard Ravitch. The card would replace the tokens that were, at the time, used to pay transit fares. This plan was generally supported by the public. In 1984, Ravitch's successor Bob Kiley said that he would try to create a system for the new farecards within the next four years. However, bureaucratic actions and disagreements delayed the rollout of the system. In March 1990, the MTA board voted to allocate funding for the magnetic fare collection system. Three months later, the New York state legislature voted to allow the MTA to proceed for its plans for the new system. By 1991, the token technology was becoming dated: almost all other transit systems were using magnetic farecards, which were found to be much cheaper than the token system. In July of that year, the MTA board approved the roll-out of the magnetic farecard system. The MTA opened a request for bids to furnish and operate the farecard system, and Cubic Transportation Systems offered the lowest bid at $100 million.
On October 30, 1992, the installation of Automated Fare Collection turnstiles began. The farecard system was given the name MetroCard by April 1993. At the time, the first subway stations were supposed to receive MetroCard-compatible turnstiles before year's end, and buses were scheduled to be retrofitted with MetroCard collection equipment by late 1995. On June 1, 1993, MTA distributed 3,000 MetroCards in the first major test of the technology for the entire subway and bus systems. Less than a year later, on January 6, 1994, MetroCard-compatible turnstiles opened at Wall Street on the IRT Lexington Avenue Line () and Whitehall Street–South Ferry on the BMT Broadway Line (). All MetroCard turnstiles were installed by May 14, 1997, when the entire bus and subway system accepted MetroCard.
On September 28, 1995, buses on Staten Island started accepting MetroCard, and by the end of 1995, MetroCard was accepted on all New York City Transit buses.
Before 1997, the MetroCard design was blue with yellow lettering. These blue cards are now collector's items. On July 4, 1997, the first free transfers were made available between bus and subway at any location with MetroCard. This program was originally billed as MetroCard Gold. Card colors changed to the current blue lettering on goldenrod background. On January 1, 1998, bonus free rides (10% of the purchase amount) were given for purchases of $15 or more. On July 4, six months later, 7-Day and 30-Day Unlimited Ride MetroCards were introduced, at $17 and $63 respectively. A 30-day Express Bus Plus MetroCard, allowing unlimited rides on express buses in addition to local buses and the subway, was also introduced at $120. The 1-Day Fun Pass was introduced on January 1, 1999, at a cost of $4. The debut of the MetroCard allowed the MTA to add bonus fare incentives, such as free bus transfers to other buses or subways. Half of the ridership increase between 1997 and 1999 was attributed to these incentives.
The first MetroCard Vending Machines (MVMs) were installed on January 25, 1999, in two stations, and by the end of 1999 347 MVMs were in service at 74 stations. On April 13, 2003, tokens were no longer sold. Starting May 4, 2003, tokens were no longer accepted, except on buses. The following fare increases were implemented:
Base fare increased from $1.50 to $2.00
1-Day Unlimited MetroCard fare increased from $4 to $7
7-Day Unlimited MetroCard fare increased from $17 to $21
30-day Express Bus Plus was replaced with a 7-day Express Bus Plus card, which cost $33 each.
30-Day Unlimited MetroCard fare increased from $63 to $70
The bonus for pay-per-ride increased to 20% of the purchase amount for purchases of $10 or more
Tokens would be phased out, but for the next two months they acted as $1.50 credit towards a $2 bus ride.
On February 27, 2005, another fare hike occurred:
7-day Express Bus Plus increased by $8, to $41.
7-Day Unlimited increased by $3, to $24.
30-Day Unlimited increased by $6, to $76.
On April 1, 2007, MetroCard started to be accepted by the Westchester Bee-Line Bus System as all of its buses were now equipped with new fareboxes that could accept MetroCard.
On March 2, 2008, another set of fare increases was implemented:
1-Day Unlimited fare increased by 50 cents, to $7.50.
7-Day Unlimited fare increased by $1, to $25.
14-Day Unlimited was introduced for $47.
30-Day Unlimited increased by $5, to $81.
The bonus for pay-per-ride decreased to 15% of the purchase amount for purchases of $7 or more.
On June 28, 2009, the agency had its second fare hike in as many years:
The base fare and single-ride ticket increased by 25 cents, to $2.25.
1-Day Unlimited fare increased by 75 cents, to $8.25.
7-Day Unlimited fare increased by $7, to $27.
7-Day Express Bus Plus fare increased by $4, to $45.
14-Day Unlimited fare increased by $4.50, to $51.50.
30-Day Unlimited increased by $8, to $89.
The minimum purchase for a pay-per-ride bonus rose to $8.
On December 30, 2010, the bonus value for Pay-Per-Ride decreased to 7% for every $10, and the 1-Day Fun Pass and the 14-Day Unlimited Ride were discontinued altogether. Additionally:
7-Day Unlimited fare increased by $2, to $29.
7-Day Express Bus Plus fare increased by $5, to $50.
30-Day Unlimited fare increased by $15, to $104.
In 2012, the MTA allowed advertisements to be printed on the fronts of MetroCards. The backs of MetroCards had already been used for advertisements since 1995. This change meant that advertisers could remove the MTA logo from the fronts of MetroCards.
As a result of Hurricane Sandy in October 2012, three free transfers were offered on the MetroCard. The first was between the Q22, the Q35, and the at the Flatbush Avenue–Brooklyn College subway station. The second between the Q22, either the Q52 Limited or the Q53 Limited, and the at the Rockaway Boulevard station. Finally, a three-hour transfer window applied from transfers from any subway station to the Q22 or Q113 routes of MTA Bus, and then to the n31, n32, and n33 routes of NICE.
On December 19, 2012, the MTA voted for the following fare increases:
Base fare and single-ride ticket increased by 25 cents, to $2.50.
7-Day Unlimited MetroCard fare increased by $1, to $30.
30-Day Unlimited MetroCard fare increased by $8, to $112.
The bonus for a pay-per-ride MetroCard decreased from 7% to 5% but the cutoff for the bonus decreased from $10 to $5.
Starting February 20, 2013, people were able to refill cards with both time and value, so that when a MetroCard is filled with both an unlimited card and fare value, the unlimited ride portion is used first where applicable. If not started already, the unlimited ride period would begin when the card is next used, and when the unlimited period expires, the regular fare would be charged. On March 3, 2013, a $1 fee was imposed on new card purchases in-system in order to reduce the number of discarded MetroCards. However, MetroCards purchased through the Extended Sales retail network carry no new card fee.
On March 22, 2015, the MTA voted for the following fare increases:
Base Fare increased by 25 cents, to $2.75;
Express Bus fare increased, to $6.50;
7-Day Unlimited fare increased by $1, to $31;
7-Day Express Bus Plus fare increased by $7.25, to $57.25;
30-Day Unlimited increased by $4.50, to $116.50;
Single Ride ticket increased by 50 cents, to $3.00; and:
the bonus for a pay-per-ride MetroCard was increased to 11%.
On March 19, 2017, the following fare increases went into place:
7-Day Unlimited fare increased by $1, to $32;
7-Day Express Bus Plus fare increased by $2.25, to $59.50;
30-Day Unlimited increased by $4.50, to $121; and
the bonus for a pay-per-ride MetroCard was reduced from 11% to 5%.
On October 23, 2017, it was announced that the MetroCard would be phased out and replaced by OMNY, a contactless fare payment system also by Cubic, with fare payment being made using Apple Pay, Google Wallet, debit/credit cards with near-field communication enabled, or radio-frequency identification cards. All buses and subway stations would use the OMNY system by 2020. However, support of the MetroCard is slated to remain until 2023.
In mid-2018, city officials tentatively agreed to start a program in which they would provide half-fare MetroCards to almost 800,000 New York City residents living below the federal poverty line. The program would start in January 2019, and the New York City allocated $106 million in fiscal year 2019 to subsidize the half-fare MetroCards for at least six months. After uncertainty over whether the program would be implemented, the half-fare MetroCards were rolled out starting on January 4, 2019. Initially, the reduced-fare MetroCards would be rolled out to 30,000 residents, though another 130,000 New Yorkers receiving SNAP benefits would also be allowed to receive the half-fare MetroCards in April 2019. However, in the revised plan, only a portion of the originally projected 800,000 residents (around 20%) would be eligible for the reduced-fare cards.
On April 21, 2019, the following fare increases went into place:
Express Bus fare increased by 25 cents, to $6.75;
7-Day Unlimited fare increased by $1, to $33;
7-Day Express Bus Plus fare increased by $2.50, to $62;
30-Day Unlimited fare increased by $6, to $127; and
the bonus for a pay-per-ride MetroCard was eliminated.
In August 2023, the following fare increases went into place:
Base Fare increased by 15 cents, to $2.90
Express Bus fare increased, to $7.00
7-Day Unlimited fare increased to $34
7-Day Express Bus Plus fare increased to $64.00
30-Day Unlimited fare increased to $132
Single Ride ticket increased by 25 cents, to $3.25
The MetroCard itself costs $1.
Technology
During a swipe, the MetroCard is read, re-written to, then check-read to verify correct encoding.
Each MetroCard stored value card is assigned a unique, permanent ten-digit serial number when it is manufactured. The value is stored magnetically on the card itself, while the card's transaction history is held centrally in the Automated Fare Collection (AFC) Database. When a card is purchased and fares are loaded onto it, the MetroCard Vending Machine or station agent's computer stores the amount of the purchase onto the card and updates the database, identifying the card by its serial number. Whenever the card is swiped at a turnstile, the value of the card is read, the new value is written, the customer is let through, and then the central database is updated with the new transaction as soon as possible. Cards are not validated in real time against the database when swiped to pay the fare. The AFC Database is necessary to maintain transaction records to track a card if needed. It has actually been used to acquit criminal suspects by placing them away from the scene of a crime. The database also stores a list of MetroCards that have been invalidated for various reasons. Reasons include the MetroCard being lost, stolen, expired student, or an expired monthly card, and it distributes the list to turnstiles in order to deny access to a revoked card.
The older blue MetroCards were not capable of the many kinds of fare options that the gold ones currently offer. The format of the magnetic stripe used by the blue MetroCard offered very little other than the standard pay-per-swipe fare. Gold MetroCards allow groups of people (up to four) to ride together using a single pay-per-swipe MetroCard. The gold MetroCard keeps track of the number of swipes at a location in order to allow those same number of people to transfer at a subsequent location, if applicable. The MetroCard system was designed to ensure backward compatibility, which allowed a smooth transition from the blue format to gold.
Cubic later used the proprietary MetroCard platform to create the Chicago Card and Tren Urbano's fare card, which are physically identical to the MetroCard except for the labeling.
Physical attributes
Dimensions: ; thickness
Material: Polyester
Card types
SingleRide Ticket
The SingleRide Ticket (introduced to replace subway tokens and single cash fares) is a piece of paper with a magnetic strip on the front, and with the date and time of purchase stamped on the back. They cost $3.25 for one subway or local bus ride, with one free transfer allowed between buses, issued by the bus operator upon request. SingleRide Tickets do not allow transfers between subways and buses. SingleRide tickets can only be purchased at MetroCard Vending Machines, which are usually located within subway stations, and expire two hours from time of purchase. Because of these limitations, SingleRide Tickets are not frequently used, having been used by only 3% of subway riders in 2009.
Although the Pay-Per-Ride MetroCard is accepted on PATH, the regular SingleRide ticket is not. However, a PATH SingleRide ticket is available from MVMs in PATH stations for $2.75, valid for 2 hours and only on PATH. PATH also accepts 2-Trip PATH MetroCards, which cost $5.50 and are also valid only on PATH.
Pay-Per-Ride MetroCard
The Pay-Per-Ride MetroCard costs $1, and can be filled with an initial value in any increment between $5.80 and $80, though vending machines only sell values in multiples of 5 cents. Cards can be refilled in 1 cent increments at station booths (formerly called token booths), and in 5 cent increments at vending machines. A MetroCard holder can spend up to $80 in one transaction and up to a total value of $100. Pay-Per-Ride MetroCards can also be filled with unlimited ride time in 7- or 30-day increments. As of 2022, station booths no longer do any MetroCard transactions.
The Pay-Per Ride MetroCard is accepted on the New York City Subway; MTA express, local, limited, and Select Bus Service buses; and the Staten Island Railway. Outside agencies also accept the MetroCard, including Nassau Inter-County Express; the PATH, operated by the Port Authority of New York and New Jersey; the AirTrain JFK, operated by the Port Authority; the Roosevelt Island Tramway; and the Westchester County Bee-Line Bus System. However, PATH does not accept reduced fare MetroCard.
Pay-Per-Ride MetroCards deduct different values depending on which service is used. Subway, Staten Island Railway, Roosevelt Island Tramway, or local/limited/Select bus uses, cost $2.90 per trip and usually allow one valid transfer, though two transfers may be allowed depending on which routes are being used (see below). Although the PATH charges $2.75 as well, it does not offer any free transfers. A ride on an MTA express bus costs $7.00, with transfers allowed to or from the subway, Staten Island Railway, or non-express MTA buses. The BxM4C Bee-Line Bus deducts $7.50 per trip, and no free or discounted transfers are allowed to or from that route. The AirTrain JFK costs $8.50 per trip if the passenger enters or leaves at Jamaica or Howard Beach–JFK Airport stations.
Transfers are available within two hours of initial entry, with the following structure:
One free transfer from
subway to local bus
bus to subway
bus to local bus
express bus to express bus
bus or subway to Staten Island Railway
subway to subway between the Lexington Avenue–59th Street () stations and the Lexington Avenue–63rd Street () station or between Junius Street () station and Livonia Avenue () station
Two consecutive free transfers are available with the MetroCard for certain transfers. The transfers must be made within two hours of each other (e.g. when one makes the first transfer, they have two hours to make the second transfer).
Between Staten Island bus routes crossing the Staten Island Railway, through St. George Ferry Terminal, and then any MTA local bus or NYC subway service below Fulton Street in Lower Manhattan.
Between certain bus routes as specified in
$4.10 for each local bus or subway to express bus transfer.
Transfers with coins (pennies and half-dollar coins not accepted) are good for use on one connecting local bus route (restrictions apply).
Customers transferring to suburban buses from another system with a lower base fare must pay the difference between the fare on the first bus and the fare on the second bus.
No transfers to the BxM4C.
No free transfer between PATH and NYC Subway, Bus and MTA Bus.
Up to 4 people can ride together on a single Pay-Per-Ride MetroCard, with one free transfer granted.
Expired card balance may be transferred to a new card at any MetroCard Vending Machine, up to one year after expiration. After one year the card must be sent to the Customer Claims area of the MTA.
EasyPayXPress MetroCard
The EasyPayXPress MetroCard functions like a pay per ride or unlimited MetroCard, but is automatically refilled from a linked credit or debit card. An EasyPayXpress account is opened with either $30 or a 30-day unlimited balance of $121. , another $45 is automatically added for Pay-Per-Ride customers when balance drops below $20. To reduce this, a one-time payment may be made online before the balance drops below $20. All rules for standard pay per ride or unlimited cards apply, and EasyPay customers can review the account and ride usage online. Reduced-fare EasyPay version converts from Pay-Per-Ride to Unlimited rides (during that billing cycle) once the value of fares used meet or exceed the cost of a reduced-fare 30-Day Unlimited Ride card. Express bus fares do not contribute, and EasyPay cannot be used on PATH trains.
AirTrain JFK Discount MetroCard
The AirTrain JFK Discount MetroCard offers 10 trips on AirTrain JFK at $26.50. This card can only be purchased at specially marked MetroCard Vending Machines. It can be refilled, and once done so, becomes a Pay-Per-Ride MetroCard. However, although the AirTrain fare is also payable using a regular Pay-Per-Ride MetroCard, no discount is given for Pay-Per-Ride cards. There is also an unlimited-ride 30-day card that costs $40 and is only valid on AirTrain JFK.
Unlimited MetroCard
, four types of Unlimited-ride MetroCards are sold:
7-Day Unlimited Ride Card, $34 for unlimited subway and local bus rides until midnight on the seventh day following first usage.
30-Day Unlimited Ride Card, $132 for unlimited subway and local bus rides until midnight on the thirtieth day following first usage.
7-Day Express Bus Plus Card, $64 for unlimited express bus, local bus, and subway rides until midnight on the seventh day following first usage.
30-Day AirTrain JFK Unlimited Ride Card, $40 for unlimited trips on the AirTrain (operated by the Port Authority of New York and New Jersey) until midnight on the thirtieth day from first usage. This card can only be purchased at specially marked MetroCard Vending Machines at the Howard Beach–JFK Airport () or Sutphin Boulevard–Archer Avenue–JFK Airport () stations and at MetroCard vendors in JFK Airport. There are no transfer privileges with this card as it only works on the AirTrain. This is the only unlimited card accepted on the AirTrain.
Any Unlimited Ride Card cannot be used at the same subway station or bus route for 18 minutes after it is swiped. Every MetroCard can be refilled in increments of 7 or 30 days' worth of unlimited ride time, or with pay-per-ride value, but time is used before value unless the time on the card cannot be applied to the ride taken. The 7 Day Express Bus Plus card is the only unlimited card that can be used on express buses. Unlimited rides cannot be applied to non-MTA transit systems such as the PATH or AirTrain JFK; to use these systems that require a value-based fare, riders can load money on their Unlimited Ride MetroCard by selecting "Add Value" when refilling at a MetroCard Vending Machine or at a station booth. Turnstiles for these systems will simply deduct the fare from the value portion of the MetroCard. 30-Day Unlimited and 7-Day Express Bus Plus Cards that are purchased using a credit, debit or ATM card from a MetroCard vending machine can be reported lost or stolen to receive a pro-rated credit for the card.
Standard 7- and 30-day unlimited cards are accepted on MTA New York City Subway; non-express buses from either the MTA, NICE, or Bee-Line; the Roosevelt Island Tramway; and the Staten Island Railway. 7-Day Express Bus Plus is accepted on MTA express buses. The AirTrain JFK only accepts the Unlimited AirTrain JFK card.
Student MetroCard
The Student MetroCard was issued to New York City public and private school students who live within the city limits. It allowed free access to the NYCT buses and trains, depending on the distance traveled between their school and their home. The card program was managed by the NYCDOE Office of Pupil Transportation. In NYC, these cards were replaced by Student OMNY cards. In Nassau County, Student MetroCards are issued by individual schools which have pre-paid for the cards. In Westchester County, cards are also issued, but cost $58 per month, or $580 a school year.
The DOE issues different colors of cards to students who live in New York City. Orange cards are given to students who are in grade K-6. Green cards are given to students who are in grades 7–12. Student MetroCards are allowed on the New York City Subway, non-express MTA buses, and the Staten Island Railway. Formerly, there was also a half-fare card that could only be used on non-express buses, discontinued in mid-2019. Red cards are issued to students and parents when there is a school bus work stoppage. Blue and purple cards are issued to Nassau County students and are only allowed to use the cards on NICE buses. Up to three trips per day may be made on student MetroCards, though four-trip MetroCards can be authorized individually for students who must make more than one transfer between home and school.
Students who receive a student MetroCard must live:
More than 0.5 miles away if they are in grades K–2
More than 1.0 miles away if they are in grades 3–6
More than 1.5 miles away if they are in grades 7–12
In May 2019, the MTA voted to phase out the half-fare student MetroCard and distribute only full-fare cards for students who qualify for a MetroCard.
Disabled/Senior Citizen Reduced-Fare MetroCard
Senior citizen MetroCards are received via application or by submitting the application in person with required ID and copies of proof of age at the NYC Transit Customer Service Center at 3 Stone St in lower Manhattan and act as a combination photo ID and MetroCard. It allows half-fare within the MTA system, and on express buses during off-peak hours only. Half fare is also available on the 7-day and 30-day Unlimited MetroCards. "Autogate" cards are issued to persons with mobility impairments and are accepted at wheelchair doors at selected stations. The card back is color-coded to indicate the gender of the card holder, and the card face is marked with "Photo ID Pass". Later issues of Senior Citizen and Disability MetroCards are uncolored (all white with black printing on back with photo, gold face remains unchanged) for gender neutral requests.
Temporary replacement cards are purple with no photo, or blue for Autogate MetroCard holders, and the value cannot be refunded if the original card is stolen or lost. A Senior & Disabled Reduced-fare EasyPay (automatic refill) card is also available.
This type of card is accepted everywhere the Pay-Per-Ride or time-based MetroCard is, with two exceptions: it is not valid on the PATH, and it is not valid for ticket purchase on New York City-bound LIRR and Metro-North trains in the morning. Reduced-Fare MetroCards (in any variety) are also not accepted at PATH stations. Reduced fare customers who do not have a MetroCard may purchase a full-fare round trip MetroCard from a subway station agent by presenting proof of eligibility.
This type of card caused complaints because it took up to three months to replace.
Fair Fares MetroCard
The Fair Fares MetroCard pilot program was implemented in January 2019. These are distributed by Fair Fares NYC, which sends letters to eligible residents that meet the income criteria, including veteran students, New York City Housing Authority residents, City University of New York students, and residents who receive benefits from the Department of Social Services. These residents must then register online to receive the Fair Fare MetroCard. Holders of the Fair Fare MetroCard can purchase Pay-Per-Ride or time-based fares at half the regular price. This type of card is accepted only on local/limited/Select buses, the subway, and the Staten Island Railway.
Emergency services
An emergency MetroCard is carried by police officers, firefighters, and emergency medical personnel while on duty so they can access the subway system during an emergency.
Fares
MetroCard Bus Transfer
The MetroCard Bus Transfer is issued upon request to passengers who pay cash fares on buses accepting MetroCard. The transfer is inserted into the fare box on the second bus, which retains it. Westchester Bee Line bus system and Nassau Inter-County Express and MTA New York City Transit bus is free to transfer from one bus to another bus that is accepted with MetroCard. The bus transfer is paper like the SingleRide Metrocard. This transfer does not grant cash customers subway access.
For suburban transfers, if the fare paid to get the transfer is less than that required on the second bus, the difference must be paid on boarding. For transfers from NICE to New York City Transit, no step up fee is required.
The predecessor to the MetroCard bus transfer was the original bus transfer. These paper tickets allowed bus to bus transfers. Available in pads of several different colors for use at different times, boroughs or directions, they would be torn at a certain time-marked line to indicate when the transfer would expire. A version of this still exists today as the "General Order Transfer" (aka "block ticket") which is provided to customers as they leave the subway system during service disruptions to re-enter the system at another point (often via a shuttle bus).
Purchase options
All new MetroCard purchases are charged a $1 fee, except to reduced fare customers and those exchanging damaged/expired cards. This purchase fee does not apply to MetroCard refills.
Subway station booths
As of 2022, booths no longer handle any transactions, and station agents have been reassigned to other functions within the station. Prior to this booths staffed by MTA station agents (at specified time periods) are located in all MTA subway stations. Every type of MetroCard could be purchased at a booth, with the exception of the SingleRide ticket (purchased at the MetroCard Vending Machine) and MetroCards specific to other transit systems (AirTrain JFK and PATH). All booth transactions had to be in cash.
MetroCard vending machines
MetroCard Vending Machines (MVMs) are located in all subway stations, PATH stations (with the added ability to reload SmartLink cards), Staten Island Ferry terminals, Roosevelt Island Tramway stations, and the Hempstead Transit Center, Eltingville Transit Center, and Central Terminal at LaGuardia Airport.
MVMs debuted on January 25, 1999, and are found in two models. Standard MVMs accept cash, credit cards, and debit cards, and are located in every subway station. Cash transactions are required for purchases of less than $1, and they can return up to $9 in coin change (this amount was changed in later years to $6). MVMs can also reload previously issued MetroCards. MetroCard Express Machines (MEMs) are smaller MVMs that only accept credit and ATM/debit cards. Both models allow customers to purchase any type of MetroCard through a touchscreen. The machines also comply with the Americans with Disabilities Act of 1990, through use of Braille and a headset jack: audible commands for each menu item are provided once a headset is connected and the proper sequence is keyed through the keypad; all non-visual commands are then entered via the keypad instead of the touchscreen. The MEMs and MVMs are geared to allow a maximum of 2 transactions per day when payment is made by either credit or debit card. PATH fare vending machines (only in PATH stations) can dispense MetroCards. MetroCards that have expired can be exchanged using a MVM or MEM if done within one year of the expiration date printed on the back of the card. This is done by using the Refill option on the machine screen. Any cash value that is left on the expired card will be transferred to the new card. No fee is charged for a new MetroCard in this instance.
MetroCard bus and van
A number of MetroCard sales vans and a MetroCard bus (a retired bus converted for sales duty) routinely travel to specific locations in New York City and Westchester County, stopping for a day (or half a day) at the announced locations. MetroCards can be purchased or refilled directly from these vehicles. Reduced-fare MetroCard applications can also be processed on the bus, including taking photographs for these cards.
The MetroCard van serves all five boroughs and Westchester County, while the MetroCard bus serves Manhattan, the Bronx, Queens, and parts of Brooklyn.
Neighborhood MetroCard merchants
Vendors can apply to sell MTA fare media at their business. Only presealed, prevalued cards are available, and no fee is charged. A comprehensive listing of neighborhood MetroCard merchants can be found on the MTA website.
Commuter railroad ticket vending machines
Ticket vending machines (TVMs) for the MTA's two commuter railroad systems, Long Island Rail Road and Metro-North Railroad, offer the option to purchase combined tickets/passes and MetroCards. A $5.50 MetroCard is available with a round-trip ticket, and a $50 MetroCard is available with a monthly pass. In addition, the machines sell separate $25 MetroCards. TVMs at Jamaica station and Penn Station sell AirTrain JFK monthly passes on the back of LIRR tickets. All cards sold from these machines are of thick paper stock, not the normal plastic.
Beginning in 2007, with the start of the S89 bus service, a combined Hudson–Bergen Light Rail (HBLR) monthly pass and monthly MetroCard became available at NJ Transit ticket vending machines at HBLR stations.
Future
In 2006, the MTA and Port Authority announced plans to replace the magnetic strip with smart cards.
On July 1, 2006, MTA launched a six-month pilot program to test the new contact-less smart card fare collection system, initially ending on December 31, 2006, but extended until May 31, 2007. This program was tested at all stations on the IRT Lexington Avenue Line and at four stations in the Bronx, Brooklyn and Queens. The testing system utilized Citibank MasterCard's Paypass keytags. This smart card system was intended to ease congestion near the fare control area by reducing time spent paying for fare. MTA and other transportation authorities in the region said they would eventually implement it system-wide.
OMNY
In October 2017, MTA signed a $573 million contract with Cubic Transportation Systems for OMNY (short for One Metro New York), a new fare payment system. This will use the contactless payment system, with riders waving or tapping credit or debit bank cards, smartphones, and/or MTA-issued smart cards to pay their fare. This contactless system was originally developed by Transport for London at a cost of £11 million (at the time equivalent to around $14 million), before being licensed to Cubic for worldwide sale. MTA expects to spend at least six years rolling out the system, with new electronic readers and vending machines. The new fare system would be rolled out on a limited basis in May 2019. It was intended that by 2024, the MetroCard would be phased out entirely, although this target has not been met.
Unauthorized resale and scams
The MetroCard system is susceptible to various types of unauthorized resale, colloquially known as "selling swipes".
At times, this may involve individuals charging to swipe another commuter into the subway system at a discount below the official fare, either by using an "unlimited ride" MetroCard, or by manipulating a spent MetroCard to obtain an extra, unpaid ride. A 2004 press release from New York State Senator Martin J. Golden claims these behaviors cost the MTA $260,000 a year.
So-called 'swipers' reportedly may secure customers by maliciously damaging the coin and bill acceptor mechanisms of metrocard vending machines Nearly half of broken vending machines were in Manhattan, and the MTA spent $26.5 million on MVM repairs as of 2017. An 18-minute delay between uses of an "unlimited ride" MetroCard at any given station, and the expense of unlimited ride MetroCards, have historically limited their use for selling swipes.
More commonly, "swipers" use a technique which involves bending a spent MetroCard in a precise way that then allows a further use of that MetroCard when swiped and unkinked according to a specific procedure at a turnstile. Swipers employ this procedure to sell discount entry to the subway; some riders simply use the technique to garner free subway entry themselves. The bend purportedly damages the magnetic stripe on the MetroCard which indicates it no longer has value, prompting the turnstile reader to defer to a back-up field which indicates that the metrocard has one remaining fare. When the technique was discovered, it could be performed an unlimited number of times with the same MetroCard. However, a software correction soon limited the technique to just once per used MetroCard, in which a turnstile computer which had deferred to that "backup" field would require the MetroCard be swiped additional times through the reader/writer before granting entry so any lingering indication of value could be deleted from the card, making it impossible to manipulate a given MetroCard in the same way once again.
Criminal charges leveled against those using this bent-MetroCard technique have included petit larceny and, in a state law introduced specifically to target swipers in the year 2006, with "unauthorized sale of transportation services." As early as 2001, however, police and prosecutors began to charge people bending MetroCards to seek free rides (either to sell, or for personal use) with various forms of forgery.
While misdemeanor forgery charges have been used in a number of jurisdictions, the Manhattan District Attorney's Office championed felony forgery charges for those in possession of manipulated metrocards, including "criminal possession of a 'forged instrument' in the 2nd Degree", a felony. A representative of that office successfully defended the charge to the state's highest court, the New York State Court of Appeals, in a case decided in 2009. Critics have argued, however, that the court's decision is based on an incomplete—and possibly incorrect—understanding of MetroCard technology, calling to question the status of a bent metrocard as a "forged instrument". The MetroCard technology has no public documentation, and has never been made available to criminal defendants who might dispute claims that a simple bend to a MetroCard alters its data as read by a turnstile computer in the way claimed by Manhattan prosecutors. It is unclear, for example, why a bent MetroCard cannot be used to obtain an unpaid ride on a New York City bus if simply bending a MetroCard can actually alter how it is read by a subway turnstile computer as prosecutors claim. One researcher has argued that a bent MetroCard must be subject to further procedures in order to be seen by the turnstile computer as legitimate, which requires both concealing data from the turnstile computer with a bend, as well as having fresh data written to the MetroCard by the turnstile computer itself. Because a bent MetroCard will not actually appear legitimate to a turnstile computer without further steps to allow the turnstile computer to write that fresh data, this casts doubt on the claim that a bent MetroCard – often cited as evidence in the prosecutions of swipers – actually constitutes a "forged instrument" as defined in New York State law.
A $1 fee on new MetroCards imposed in 2013 significantly curtailed the bent-MetroCard form of selling swipes. The fee motivated riders to keep and refill their existing MetroCards, undermining the vast supply of discarded spent MetroCards from which swipers previously drew as their stock-in-trade. Nonetheless, people continue to sell swipes of bent MetroCards which have been discarded. Swipers continue to be prosecuted under forgery laws, according to research published in 2019.
The MetroCard has resisted digital duplication through software. The MetroCard has a magnetic stripe, but both the track offsets and the encoding differ from standard Magstripe cards. It is a proprietary format developed by the contractor Cubic. Off-the-shelf reader/writers for the standard cards are useless to read from or write to MetroCards without mechanical modification and custom software. Self-identified hackers have had success decoding MetroCard data by treating Metrocard contents as sound, and converting its contents to binary using a computer sound card, inferring the role of data fields by comparing MetroCards with known properties, and developing custom Linux software to decode MetroCard data. Moreover, MetroCard data has been duplicated to other media, also by treating it as sound, using an eight-track tape player. While duplicates may be usable to enter the subway in the short term, they are likely to be invalidated after the AFC database discovers imbalance between fares purchased for a MetroCard with a certain serial number, and fares used from one or more MetroCards bearing that serial number.
Limited editions
Over the years, the MTA has issued limited-edition MetroCards in honor of certain events, people, or structures.
Back side designs
For much of the MetroCard's history, images were printed only on the back side of MetroCards. These have included cards with the Statue of Liberty, the New York City bid for the 2012 Summer Olympics, a Solomon R. Guggenheim Museum exhibit, and the Circle Line ferry. Sporting events have also been commemorated, including the Subway Series, the 2014 Super Bowl, and the 2014–15 season of the Brooklyn Nets.
In 2017, the MTA started issuing Supreme-branded MetroCards at eight subway stations. The Supreme-branded cards were popular, and there were reports that some were resold for hundreds of dollars. The MTA issued MetroCards featuring Mariska Hargitay, the main actor in the TV series Law & Order: Special Victims Unit, in 2024 to celebrate the show's 25th anniversary.
Front side designs
The MTA started allowing front side advertising in 2012. One of the earlier front side designs was an I Love New York card first sold in October 2013. Three hundred thousand cards were printed in remembrance of Hurricane Sandy the previous year.
Starting in December 2018, the MTA started issuing 250,000 Game of Thrones-themed MetroCards at Grand Central–42nd Street, in honor of the show's final season. The cards came in four designs. Starting in May 2019, coinciding with the opening of the Memorial Glade at the National September 11 Memorial & Museum, the MTA issued 250,000 MetroCards with images of first responders at the World Trade Center site after 9/11. The MetroCards were issued at ten subway stations: six in Lower Manhattan and four high-traffic stations in midtown and Brooklyn. In June 2019, the MTA celebrated Stonewall 50 - WorldPride NYC 2019 with LGBT pride-themed MetroCards.
In November 2020, the MTA celebrated Veterans Day with Veterans Day themed MetroCards. The MetroCards were available at six stations: two in Brooklyn, one in Queens, two in Midtown Manhattan, and one in The Bronx. In 2023, the MTA issued special Cam'ron, LL Cool J, Rakim, and Pop Smoke MetroCards. In 2024, the MTA issued Ice Spice MetroCards to celebrate the launch of Ice Spice's first album. That May, the MTA announced that two final front-side MetroCard designs would be issued, as the MTA was in the process of retiring the MetroCard itself. The second-to-last commemorative card was themed to Olivia Rodrigo and was sold starting in October 2024. The last promotional Metrocard, collaborating with Instagram, features social media stars "New York Nico", "SubwayTakes" and "Overheard NY" were sold starting on December 9, 2024.
Notes
References
External links
Fare collection systems in the United States
Bus transportation in New York City
Products introduced in 1993
Metropolitan Transportation Authority
New York City Subway fare payment
Vending machines
MTA Regional Bus Operations
PATH (rail system)
de:New York City Subway#Tokens und MetroCard | MetroCard | [
"Engineering"
] | 9,158 | [
"Vending machines",
"Automation"
] |
362,151 | https://en.wikipedia.org/wiki/OMAR%20Mine%20Museum | The OMAR Mine Museum in Kabul, Afghanistan, contains a collection of 51 types of land mines out of the 53 that have been used in that country. OMAR is an acronym for the Organization for Mine Clearance and Afghan Rehabilitation.
Mine collection
The collection includes unexploded ordnance, cluster bombs and airdrop bombs used by the War in Afghanistan. The museum educates school groups to detect and avoid unexploded ordnance including landmines and cluster bomblets from historic and ongoing Afghan wars. The museum was seriously damaged in a July 1, 2019 attack.
The museum also displays a variety of other military hardware from wars fought in Afghanistan over the recent decades, including artillery, surface-to-air missiles, and a collection of Soviet military aircraft.
For security reasons, the museum is not open for casual visitors. All appointments must be made through the main OMAR office.
Aircraft on display
Su-7
Yak-40
L-39
Mi-8
MiG-17
An-2
Mi-24
Yak-11
Gallery
See also
List of museums in Afghanistan
References
Organisation for Mine Clearance & Afghan Rehabilitation
Aviation Museum
External links
Blog entries describing visits to the museum:
The Velvet Rocket.com: OMAR Mine Museum
TravelBlog.org: OMAR Mine Museum
Blog.vm.ee—Our Man in Kabul: OMAR Mine Museum
Buildings and structures in Kabul
Military and war museums
Museums in Afghanistan
Aerospace museums
Area denial weapons
Explosive weapons | OMAR Mine Museum | [
"Engineering"
] | 286 | [
"Area denial weapons",
"Military engineering"
] |
362,193 | https://en.wikipedia.org/wiki/22%20%28number%29 | 22 (twenty-two) is the natural number following 21 and preceding 23.
In Mathematics
22 is a semiprime, a Smith number, and an Erdős–Woods number. is a commonly used approximation of the irrational number , the ratio of the circumference of a circle to its diameter.
22 can read as "two twos", which is the only fixed point of John Conway's look-and-say function.
The number 22 appears prominently within sporadic groups. The Mathieu group M22 is one of 26 sporadic finite simple groups, defined as the 3-transitive permutation representation on 22 points. There are also 22 regular complex apeirohedra.
In other fields
Catch-22 (1961), Joseph Heller's novel, and its 1970 film adaptation gave rise to the expression of logic "catch-22".
In culture and religion
22 is a master number in numerology.
In weights and measures
The number of yards in a chain.
In other uses
Twenty-two may also refer to:
In French jargon, "22" is used as a phrase to warn of the coming of the police (typically " !" (In English: "5-0! Cops!")
In Spanish lottery and bingo, 22 is nicknamed after its shape.
See also
Catch 22 (disambiguation)
Notes
References
External links
Integers | 22 (number) | [
"Mathematics"
] | 281 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,201 | https://en.wikipedia.org/wiki/24%20%28number%29 | 24 (twenty-four) is the natural number following 23 and preceding 25. It is equal to two dozen and one sixth of a gross.
In mathematics
24 is an even composite number, a highly composite number, an abundant number, a practical number, and a congruent number. The many ways 24 can be constructed inspired a children's mathematical game involving the use of any of the four standard operations on four numbers on a card to get 24 (see 24 Game).
24 is also part of the only nontrivial solution pair to the cannonball problem, and the kissing number in 4-dimensional space. An icositetragon is a regular polygon with 24 sides. A tesseract has 24 two-dimensional square faces.
In religion
In Christian apocalyptic literature it represents the complete Church, being the sum of the 12 tribes of Israel and the 12 Apostles of the Lamb of God. For example, in The Book of Revelation: "Surrounding the throne were twenty-four other thrones, and seated on them were twenty-four elders. They were dressed in white and had crowns of gold on their heads."
Number of Tirthankaras in Jainism.
Number of spokes in the Ashok Chakra.
In culture
In Brazil, twenty-four is associated with homosexuality as it is the number that stands for the deer in a game known as “jogo do bicho”.
References
External links
My Favorite Numbers: 24, John C. Baez
Integers | 24 (number) | [
"Mathematics"
] | 302 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,203 | https://en.wikipedia.org/wiki/23%20%28number%29 | 23 (twenty-three) is the natural number following 22 and preceding 24.
In mathematics
Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet (7, 11, 13, 17, 19, 23). Twenty-three is also the next to last member of the first Cunningham chain of the first kind (2, 5, 11, 23, 47), and the sum of the prime factors of the second set of consecutive discrete semiprimes, (21, 22). 23 is the smallest odd prime to be a highly cototient number, as the solution to for the integers 95, 119, 143, and 529.
23 is the second Smarandache–Wellin prime in base ten, as it is the concatenation of the decimal representations of the first two primes (2 and 3) and is itself also prime, and a happy number.
The sum of the first nine primes up to 23 is a square: and the sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers.
It is the fifth factorial prime, and since 14! + 1 is a multiple of 23, but 23 is not one more than a multiple of 14, 23 is the first Pillai prime.
In the list of fortunate numbers, 23 occurs twice, since adding 23 to either the fifth or eighth primorial gives a prime number (namely 2333 and 9699713).
23 has the distinction of being one of two integers that cannot be expressed as the sum of fewer than 9 cubes of positive integers (the other is 239). See Waring's problem.
The twenty-third highly composite number 20,160 is one less than the last number (the 339th super-prime 20,161) that cannot be expressed as the sum of two abundant numbers.
Otherwise, is the largest even number that is not the sum of two abundant numbers.
23 is the second Woodall prime, and an Eisenstein prime with no imaginary part and real part of the form It is the fifth Sophie Germain prime and the fourth safe prime.
23 is the number of trees on 8 unlabeled nodes. It is also a Wedderburn–Etherington number, which are numbers that can be used to count certain binary trees.
The natural logarithms of all positive integers lower than 23 are known to have binary BBP-type formulae.
23 is the first prime p for which unique factorization of cyclotomic integers based on the pth root of unity breaks down.
23 is the smallest positive solution to Sunzi's original formulation of the Chinese remainder theorem.
23 is the smallest prime such that the largest consecutive pair of -smooth numbers (11859210, 11859211) is the same as the largest consecutive pair of -smooth numbers.
According to the birthday paradox, in a group of 23 or more randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday.A related coincidence is that 365 times the natural logarithm of 2, approximately 252.999, is very close to the number of pairs of 23 items and 22nd triangular number, 253.
The first twenty-three odd prime numbers (between 3 and 89 inclusive), are all cluster primes such that every even positive integer can be written as the sum of two prime numbers that do not exceed .
23 is the smallest discriminant of imaginary quadratic fields with class number 3 (negated), and it is the smallest discriminant of complex cubic fields (also negated).
The twenty-third permutable prime in decimal is also the second to be a prime repunit (after ), followed by and .
Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
Mersenne numbers
The first Mersenne number of the form that does not yield a prime number when inputting a prime exponent is with
On the other hand, the second composite Mersenne number contains an exponent of twenty-three:
The twenty-third prime number (83) is an exponent to the fourteenth composite Mersenne number, which factorizes into two prime numbers, the largest of which is twenty-three digits long when written in base ten:
Further down in this sequence, the seventeenth and eighteenth composite Mersenne numbers have two prime factors each as well, where the largest of these are respectively twenty-two and twenty-four digits long,
Where prime exponents for and add to 106, which lies in between prime exponents of and , the index of the latter two (17 and 18) in the sequence of Mersenne numbers sum to 35, which is the twenty-third composite number.
is twenty-three digits long in decimal, and there are only three other numbers whose factorials generate numbers that are digits long in base ten: 1, 22, and 24.
In geometry
The Leech lattice Λ24 is a 24-dimensional lattice through which 23 other positive definite even unimodular Niemeier lattices of rank 24 are built, and vice-versa. Λ24 represents the solution to the kissing number in 24 dimensions as the precise lattice structure for the maximum number of spheres that can fill 24-dimensional space without overlapping, equal to 196,560 spheres. These 23 Niemeier lattices are located at deep holes of radii in lattice points around its automorphism group, Conway group . The Leech lattice can be constructed in various ways, which include:
By means of a matrix of the form where is the identity matrix and is a 24 by 24 Hadamard matrix (Z/23Z ∪ ∞) with a = 2 and b = 3, and entries X(∞) = 1 and X(0) = -1 with X(n) the quadratic residue symbol mod 23 for nonzero n.
Through the extended binary Golay code and Witt design , which produce a construction of the 196,560 minimal vectors in the Leech lattice. The extended binary Golay code is an extension of the perfect binary Golay code , which has codewords of size 23. has Mathieu group as its automorphism group, which is the second largest member of the first generation in the happy family of sporadic groups. has a minimum faithful complex representation in 22 dimensions and group-3 actions on 253 objects, with 253 equal to the number of pairs of objects in a set of 23 objects. In turn, is the automorphism group of Mathieu group , which works through to generate 8-element octads whose individual elements occur 253 times through its entire block design.
Using Niemer lattice D24 of group order 223·24! and Coxeter number 46 = 2·23, it can be made into a module over the ring of integers of quadratic field , whereby multiplying D24 by a non-principal ideal of the ring of integers yields the Leech lattice.
Conway and Sloane provided constructions of the Leech lattice from all other 23 Niemeier lattices.
Twenty-three four-dimensional crystal families exist within the classification of space groups. These are accompanied by six enantiomorphic forms, maximizing the total count to twenty-nine crystal families. Five cubes can be arranged to form twenty-three free pentacubes, or twenty-nine distinct one-sided pentacubes (with reflections).
There are 23 three-dimensional uniform polyhedra that are cell facets inside uniform 4-polytopes that are not part of infinite families of antiprismatic prisms and duoprisms: the five Platonic solids, the thirteen Archimedean solids, and five semiregular prisms (the triangular, pentagonal, hexagonal, octagonal, and decagonal prisms).
23 Coxeter groups of paracompact hyperbolic honeycombs in the third dimension generate 151 unique Wythoffian constructions of paracompact honeycombs. 23 four-dimensional Euclidean honeycombs are generated from the cubic group, and 23 five-dimensional uniform polytopes are generated from the demihypercubic group.
In two-dimensional geometry, the regular 23-sided icositrigon is the first regular polygon that is not constructible with a compass and straight edge or with the aide of an angle trisector (since it is neither a Fermat prime nor a Pierpont prime), nor by neusis or a double-notched straight edge. It is also not constructible with origami, however it is through other traditional methods for all regular polygons.
In religion
In Biblical numerology, it is associated with Psalm 23, also known as the Shepherd Psalm. It is possibly the most quoted and best known Psalm.
Principia Discordia, the sacred text of Discordianism, holds that 23 (along with the discordian prime 5) is one of the sacred numbers of Eris, goddess of discord.
In popular culture
Film and television
In the TV series Lost, 23 is one of the 6 reoccurring numbers (4, 8, 15, 16, 23, 42) that appear frequently throughout the show.
Other fields
23 skidoo (phrase) (sometimes 23 skiddoo) is an American slang phrase popularized during the early 20th century. 23 skidoo has been described as "perhaps the first truly national fad expression and one of the most popular fad expressions to appear in the U.S".
The 23 enigma, proposed by William S. Burroughs, plays a prominent role in the plot of the Illuminatus! Trilogy by Robert Shea and Robert Anton Wilson.
The Number 23 is a 2007 film starring Jim Carrey about a man who becomes obsessed with the 23 enigma.
The number 23 is used a lot throughout the visuals and music by the band Gorillaz, who have even devoted a whole page of their autobiography Rise Of The Ogre to the 23 enigma theory.
References
External links
23 facts, 23 images, 23 gallery, and links to other 23's
Integers | 23 (number) | [
"Mathematics"
] | 2,123 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,204 | https://en.wikipedia.org/wiki/25%20%28number%29 | 25 (twenty-five) is the natural number following 24 and preceding 26.
In mathematics
It is a square number, being 52 = 5 × 5, and hence the third non-unitary square prime of the form p2.
It is one of two two-digit numbers whose square and higher powers of the number also ends in the same last two digits, e.g., 252 = 625; the other is 76.
25 has an even aliquot sum of 6, which is itself the first even and perfect number root of an aliquot sequence; not ending in (1 and 0).
It is the smallest square that is also a sum of two (non-zero) squares: 25 = 32 + 42. Hence, it often appears in illustrations of the Pythagorean theorem.
25 is the sum of the five consecutive single-digit odd natural numbers 1, 3, 5, 7, and 9.
25 is a centered octagonal number, a centered square number, a centered octahedral number, and an automorphic number.
25 percent (%) is equal to .
It is the smallest decimal Friedman number as it can be expressed by its own digits: 52.
It is also a Cullen number and a vertically symmetrical number. 25 is the smallest pseudoprime satisfying the congruence 7n = 7 mod n.
25 is the smallest aspiring number — a composite non-sociable number whose aliquot sequence does not terminate.
According to the Shapiro inequality, 25 is the smallest odd integer n such that there exist x, x, ..., x such that
where x = x, x = x.
Within decimal, one can readily test for divisibility by 25 by seeing if the last two digits of the number match 00, 25, 50, or 75.
There are 25 primes under 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
F4, H4 symmetry and lattices Λ24, II25,1
Twenty-five 24-cells with symmetry in the fourth dimension can be arranged in two distinct manners, such that
The 24-cell can be further generated using three copies of the 8-cell, where the 24-cell honeycomb is dual to the 16-cell honeycomb (with the tesseract the dual polytope to the 16-cell).
On the other hand, the positive unimodular lattice in twenty-six dimensions is constructed from the Leech lattice in twenty-four dimensions using Weyl vector
that features the only non-trivial solution, i.e. aside from , to the cannonball problem where sum of the squares of the first twenty-five natural numbers in is in equivalence with the square of (that is the fiftieth composite). The Leech lattice, meanwhile, is constructed in multiple ways, one of which is through copies of the lattice in eight dimensions isomorphic to the 600-cell, where twenty-five 24-cells fit; a set of these twenty-five integers can also generate the twenty-fourth triangular number, whose value twice over is
In religion
In Ezekiel's vision of a new temple: The number twenty-five is of cardinal importance in Ezekiel's Temple Vision (in the Bible, Ezekiel chapters 40–48).
In sports
In baseball, the number 25 is typically reserved for the best slugger on the team. Examples include Mark McGwire, Barry Bonds, Jim Thome, and Mark Teixeira.
In other fields
Twenty-five is:
The number of years of marriage marked in a silver wedding anniversary.
References
Integers | 25 (number) | [
"Mathematics"
] | 769 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,205 | https://en.wikipedia.org/wiki/26%20%28number%29 | 26 (twenty-six) is the natural number following 25 and preceding 27.
In mathematics
26 is the seventh discrete semiprime () and the fifth with 2 as the lowest non-unitary factor thus of the form (2.q), where q is a higher prime.
26 is the smallest even number n such that both n + 1 and n − 1 are composite.
With an aliquot sum of 16, within an aliquot sequence of five composite numbers (26,16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
26 is the only integer that is one greater than a square (5 + 1) and one less than a cube (3 − 1).
26 is a telephone number, specifically, the number of ways of connecting 5 points with pairwise connections.
There are 26 sporadic groups.
The 26-dimensional Lorentzian unimodular lattice II25,1 plays a significant role in sphere packing problems and the classification of finite simple groups. In particular, the Leech lattice is obtained in a simple way as a subquotient.
26 is the smallest number that is both a nontotient and a noncototient number.
26 is the number of permutations of {a, b, c, d, e} with only one ascent.
There are 26 faces of a rhombicuboctahedron.
When a 3 × 3 × 3 cube is made of 27 unit cubes (e.g. Rubik's Cube), 26 of them are viewable as the exterior layer.
A cube has 26 elements: 6 faces, 12 edges, and 8 vertices.
A 26-sided polygon is called an icosihexagon.
φ(26) = φ(σ(26)).
Properties of its positional representation in certain radixes
Twenty-six is a repdigit in base three (2223) and in base 12 (2212).
In base ten, 26 is the smallest positive integer that is not a palindrome to have a square (262 = 676) that is a palindrome.
In religion
26 is the gematric number, being the sum of the Hebrew characters () being the name of the god of Israel – YHWH (Yahweh).
26 is also the gematric number for GOD with the corresponding substitutions in English (i.e. A=1, B=2, C=3, and so on)
References
External links
Prime Curios! 26 from the Prime Pages
Integers | 26 (number) | [
"Mathematics"
] | 539 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,209 | https://en.wikipedia.org/wiki/Contact%20breaker | A contact breaker (or "points") is a type of electrical switch, found in the ignition systems of spark-ignition internal combustion engines. The switch is automatically operated by a cam driven by the engine. The timing of operation of the switch is set so that a spark is produced at the right time to ignite the compressed air/fuel mixture in the cylinder of the engine. A mechanism may be provided to slightly adjust timing to allow for varying load on the engine. Since these contacts operate frequently, they are subject to wear, causing erratic ignition of the engine. More recent engines use electronic means to trigger the spark, which eliminated contact wear and allows computer control of ignition timing.
Purpose
The purpose of the contact breaker is to interrupt the current flowing in the primary winding of the ignition coil. When the current stops flowing, the resulting collapse of the magnetic field in the primary winding induces a high voltage in the secondary winding. This causes a very high voltage to appear at the coil output for a short period—enough to arc across the electrodes of a spark plug.
Operation
The contact breaker is operated by an engine-driven cam. On an engine with a distributor, the contact breaker can be found beneath the distributor cap. The position of the contact breaker is set so that it opens (and hence generates a spark) at exactly the optimum moment to ignite the fuel/air mixture. This point is generally just before the piston reaches the top of its compression stroke. The contact breaker is often mounted on a plate that is able to rotate relative to the camshaft operating it. The plate is most typically rotated by a centrifugal mechanism, thus advancing the ignition timing (making the spark occur earlier) at higher revolutions. This gives the fuel ignition process time to proceed so that the resulting combustion reaches its maximum pressure at the proper point in the crankshaft's rotation.
Many engines are also fitted with a manifold vacuum-operated servomechanism to provide additional rotation of the plate's position (within limits), in order to advance the timing when the engine is required to speed up on demand. Advancing the ignition timing helps to prevent pre-ignition (or pinging).
Disadvantages of contact breakers
Since they open and close so often (several times with every turn of the engine on distributor-equipped engines), contact breaker points and cam followers can suffer from wear—both mechanical and pitting caused by arcing across the contacts. This latter effect is largely prevented by placing a capacitor parallel across the contact breaker—this is often referred to by the more old fashioned term condenser by mechanics. As well as suppressing arcing, it helps boost the coil output by creating a resonant LC circuit with the coil windings.
A drawback of using a mechanical switch as part of the ignition timing is that it is not very precise, needs regular adjustment of the dwell (contact) angle, and at higher revolutions, its mass becomes significant, leading to poor operation at higher engine speeds. These effects can largely be overcome using electronic ignition systems, where the contact breakers are retrofitted by a magnetic (Hall effect) or optical sensor device. However, because of their simplicity, and since contact breaker points gradually degrade instead of catastrophically failing, they are still used on aircraft engines.
See also
Ignition magneto
References
Automotive ignition systems
Automotive electrics | Contact breaker | [
"Engineering"
] | 683 | [
"Electrical engineering",
"Automotive electrics"
] |
362,212 | https://en.wikipedia.org/wiki/29%20%28number%29 | 29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number.
29 is the number of days February has on a leap year.
Mathematics
29 is the tenth prime number.
Integer properties
29 is the fifth primorial prime, like its twin prime 31.
29 is the smallest positive whole number that cannot be made from the numbers , using each digit exactly once and using only addition, subtraction, multiplication, and division. None of the first twenty-nine natural numbers have more than two different prime factors (in other words, this is the longest such consecutive sequence; the first sphenic number or triprime, 30 is the product of the first three primes 2, 3, and 5). 29 is also,
the sum of three consecutive squares, 22 + 32 + 42.
the sixth Sophie Germain prime.
a Lucas prime, a Pell prime, and a tetranacci number.
an Eisenstein prime with no imaginary part and real part of the form 3n − 1.
a Markov number, appearing in the solutions to x + y + z = 3xyz: {2, 5, 29}, {2, 29, 169}, {5, 29, 433}, {29, 169, 14701}, etc.
a Perrin number, preceded in the sequence by 12, 17, 22.
the number of pentacubes if reflections are considered distinct.
the tenth supersingular prime.
On the other hand, 29 represents the sum of the first cluster of consecutive semiprimes with distinct prime factors (14, 15). These two numbers are the only numbers whose arithmetic mean of divisors is the first perfect number and unitary perfect number, 6 (that is also the smallest semiprime with distinct factors). The pair (14, 15) is also the first floor and ceiling values of imaginary parts of non-trivial zeroes in the Riemann zeta function,
29 is the largest prime factor of the smallest number with an abundancy index of 3,
1018976683725 = 33 × 52 × 72 × 11 × 13 × 17 × 19 × 23 × 29
It is also the largest prime factor of the smallest abundant number not divisible by the first even (of only one) and odd primes, 5391411025 = 52 × 7 × 11 × 13 × 17 × 19 × 23 × 29. Both of these numbers are divisible by consecutive prime numbers ending in 29.
15 and 290 theorems
The 15 and 290 theorems describes integer-quadratic matrices that describe all positive integers, by the set of the first fifteen integers, or equivalently, the first two-hundred and ninety integers. Alternatively, a more precise version states that an integer quadratic matrix represents all positive integers when it contains the set of twenty-nine integers between 1 and 290:
The largest member 290 is the product between 29 and its index in the sequence of prime numbers, 10. The largest member in this sequence is also the twenty-fifth even, square-free sphenic number with three distinct prime numbers as factors, and the fifteenth such that is prime (where in its case, 2 + 5 + 29 + 1 = 37).
Dimensional spaces
The 29th dimension is the highest dimension for compact hyperbolic Coxeter polytopes that are bounded by a fundamental polyhedron, and the highest dimension that holds arithmetic discrete groups of reflections with noncompact unbounded fundamental polyhedra.
Notes
References
External links
Prime Curios! 29 from the Prime Pages
Integers | 29 (number) | [
"Mathematics"
] | 735 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,213 | https://en.wikipedia.org/wiki/28%20%28number%29 | 28 (twenty-eight) is the natural number following 27 and preceding 29.
In mathematics
Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors: . As a perfect number, it is related to the Mersenne prime 7, since . The next perfect number is 496, the previous being 6.
Though perfect, 28 is not the aliquot sum of any other number other than itself; thus, it is not part of a multi-number aliquot sequence. The next perfect number is 496.
Twenty-eight is the sum of the totient function for the first nine integers.
Since the greatest prime factor of is 157, which is more than 28 twice, 28 is a Størmer number.
Twenty-eight is a harmonic divisor number, a happy number, the 7th triangular number, a hexagonal number, a Leyland number of the second kind (), and a centered nonagonal number.
It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).
It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...
There are 28 convex uniform honeycombs.
Twenty-eight is the only positive integer that has a unique Kayles nim-value.
Twenty-eight is the only known number that can be expressed as a sum of the first positive integers (), a sum of the first primes (), and a sum of the first nonprimes (), and it is unlikely that any other number has this property.
There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.
There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers.
Twenty-eight is the smallest number that can be expressed as the sum of four nonzero squares in (at least) three ways: , or (see image).
In science
The fourth magic number in physics.
In other fields
Twenty-eight is:
Deriving from the 29.46 year period of Saturn's revolution around the Sun, the 28-year cycle as well as its subdivisions by 14 and 7 are supposed in astrology to mark significant turning points or sections in the course of a person's development in life. Thus, the number 28 has special significance in the culture of religious sects such as the Kadiri and the Mevlevi dervishes. The 28-beat metric pattern often used in the music compositions accompanying the main part of the Mevlevi sema ritual is called the "Devri kebir", meaning the "Big Circle" and is a reference to above astronomical facts about the year and the Saturn year.
In Quebec, François Pérusse, in one of his best-selling Album du peuple made a parody of Wheel of Fortune in which all of the letters picked by the contestant were present 28 times. As a result, 28 became an almost mythical number used by many Quebec youths, the phrase "Y'en a 28" (There are 28 [Letters]) became a running gag still used and recognized more than 15 years later.
Approximately the number of grams in an ounce, and used as such in the illegal drug trade.
References
External links
Prime Curios! 28 from the Prime Pages
Integers | 28 (number) | [
"Mathematics"
] | 720 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
362,222 | https://en.wikipedia.org/wiki/Distributor | A distributor is an electric and mechanical device used in the ignition system of older spark ignition engines. The distributor's main function is to route electricity from the ignition coil to each spark plug at the correct time.
Design
A distributor consists of a rotating arm ('rotor') that is attached to the top of a rotating 'distributor shaft'. The rotor constantly receives high-voltage electricity from an ignition coil via brushes at the centre of the rotor. As the rotor spins, its tip passes close to (but does not touch) the output contacts for each cylinder. As the electrified tip passes each output contact, the high-voltage electricity is able to 'jump' across the small gap. This burst of electricity then travels to the spark plug (via high tension leads), where it ignites the air-fuel mixture in the combustion chamber.
On most overhead valve engines, the distributor shaft is driven by a gear on the camshaft, often shared with the oil pump; on most overhead camshaft engines, the distributor shaft is attached directly to a camshaft.
Older distributor designs used a cam on the distributor shaft that operates the contact breaker (also called points). Opening the points causes a high induction voltage in the ignition coil. This design was superseded by an electronically controlled ignition coil with a sensor (usually Hall effect or optical) to control the timing of the ignition coil charging.
Ignition advance
In older distributors, adjusting the ignition timing is usually achieved through both mechanical advance and vacuum advance. Mechanical advance adjusts the timing based on the engine speed (rpm), using a set of hinged weights attached to the distributor shaft. These weights cause the breaker points mounting plate to slightly rotate, thereby advancing the ignition timing. Vacuum advance typically uses manifold vacuum to adjust the ignition timing, for example to improve fuel economy and driveability when minimal power is required from the engine.
Most distributors used on electronic fuel injection engines use electronics to adjust the ignition timing, instead of vacuum and centrifugal systems. This allows the ignition timing to be optimised based on factors other than engine speed and manifold vacuum.
Direct ignition
Since the early 2000s, many cars have used a 'coil-on-plug' direct ignition system, whereby a small ignition coil is located directly above the spark plug for each cylinder. This design means that high-voltage electricity is only present in the small distance between each coil and the spark plug. See Saab Direct Ignition.
Gallery
History
The first mass-produced electric ignition was the Delco ignition system, which was introduced in the 1910 Cadillac Model 30. In 1921, Arthur Atwater Kent Sr invented the competing Unisparker ignition system.
By the 1980s and 1990s, distributors had been largely replaced by electronic ignition systems.
See also
List of auto parts
References
Electric power distribution
Engine components
Ignition systems | Distributor | [
"Technology"
] | 565 | [
"Engine components",
"Engines"
] |
362,332 | https://en.wikipedia.org/wiki/Ficus%20rubiginosa | Ficus rubiginosa, the rusty fig or Port Jackson fig (damun in the Dharug language), is a species of flowering plant native to eastern Australia in the genus Ficus. Beginning as a seedling that grows on other plants (hemiepiphyte) or rocks (lithophyte), F. rubiginosa matures into a tree high and nearly as wide with a yellow-brown buttressed trunk. The leaves are oval and glossy green and measure from long and wide.
The fruits are small, round, and yellow, and can ripen and turn red at any time of year, peaking in spring and summer. Like all figs, the fruit is in the form of a syconium, an inverted inflorescence with the flowers lining an internal cavity. F. rubiginosa is exclusively pollinated by the fig wasp species Pleistodontes imperialis, which may comprise four cryptospecies. The syconia are also home to another fourteen species of wasp, some of which induce galls while others parasitise the pollinator wasps and at least two species of nematode. Many species of bird, including pigeons, parrots, and various passerines, eat the fruit. Ranging along the Australian east coast from Queensland to Bega in southern New South Wales (including the Port Jackson area, leading to its alternative name), F. rubiginosa grows in rainforest margins and rocky outcrops. It is used as a shade tree in parks and public spaces, and when potted is well-suited for use as an indoor plant or in bonsai.
Taxonomy
Ficus rubiginosa was described by French botanist René Louiche Desfontaines in 1804, from a type specimen whose locality is documented simply as "New Holland". In searching for the type specimen, Australian botanist Dale Dixon found one from the herbarium of Desfontaines at Florence Herbarium and one from the herbarium of Étienne Pierre Ventenat at Geneva. As Ventenat had used Desfontaines' name, Dixon selected the Florence specimen to be the type in 2001. The specific epithet rubiginosa related to the rusty coloration of the undersides of the leaves. Indeed, rusty fig is an alternate common name; others include Illawarra fig and Port Jackson fig. It was known as damun (pron. "tam-mun") to the Eora and Darug inhabitants of the Sydney basin.
In 1806, German botanist Carl Ludwig Willdenow gave it the botanical name Ficus australis in Species Plantarum, but this is a nomen illegitimum as the species already had a validly published name. That link https://www.anbg.gov.au/cgi-bin/apni?taxon_id=38740 is now this: https://id.biodiversity.org.au/instance/apni/511809. Italian botanist Guglielmo Gasparrini broke up the genus Ficus in 1844, placing the species in the genus Urostigma as U. rubiginosum. In 1862, Dutch botanist Friedrich Anton Wilhelm Miquel described Urostigma leichhardtii from material collected from Cape Cleveland, Queensland, noting it had affinities to F. rubiginosa. In 1867, he placed Urostigma as a subgenus in the reunited Ficus, which resulted in the taxon becoming Ficus leichhardtii. Miquel also described Ficus leichhardtii variety angustata from Whitsunday Island, later classified as F. shirleyana by Czech botanist Karel Domin. Queensland state botanist Frederick Manson Bailey described Ficus macrophylla variety pubescens in 1911 from Queensland, Domin later renaming it Ficus baileyana. All these taxa were found to be indistinguishable from (and hence reclassified as) F. rubiginosa by Dixon in 2001.
In a study published in 2008, Nina Rønsted and colleagues analysed the DNA sequences from the nuclear ribosomal internal and external transcribed spacers, and the glyceraldehyde 3-phosphate dehydrogenase region, in the first molecular analysis of the section Malvanthera. They found F. rubiginosa to be most closely related to the rainforest species F. watkinsiana and two rock-growing (lithophytic) species of arid northern Australia (F. atricha and F. brachypoda). They classified these species in a new series Rubiginosae in the subsection Platypodeae. Relationships are unclear and it is uncertain into which direction the group radiated (into rainforest or into arid Australia).
Joseph Maiden described variety lucida in 1902, and Bailey described variety glabrescens in 1913. Both had diagnosed their varieties on the basis of their hairlessness. Maiden described a taxon totally devoid of hair, while Bailey described his as nearly glabrous (hairless). As Bailey's description more closely matched Dixon's findings (that these variants were only partly and not completely hairless), Dixon retained Bailey's name and reclassified it as Ficus rubiginosa forma glabrescens in 2001 as it differed only in the lack of hairs on new growth from the nominate form.
Description
A spreading, densely-shading tree when mature, F. rubiginosa may reach or more in height, although it rarely exceeds in the Sydney region.
The trunk is buttressed and can reach in diameter. The bark is yellow-brown. It can also grow as on other plants as a hemiepiphyte, or high lithophyte.
Alternately arranged on the stems, the ovate (egg-shaped), obovate (reverse egg-shaped) or oval-shaped leaves are anywhere from long and wide, on -long petioles (stalks that join the leaves to stems). They are smooth or bear tiny rusty hairs. There are 16 to 62 pairs of lateral veins that run off the midvein at an angle of 41.5–84.0°, while distinct basal veins run off the midvein at an angle of 18.5–78.9°.
As with all figs, the fruit (fig) is actually an inverted inflorescence (compound flower) known as a syconium, with tiny flowers arising from the fig's inner surface into a hollow cavity. F. rubiginosa is monoecious—both male and female flowers are found on the same plant, and in fact in the same fruit, although they mature at different times. Often growing in pairs, the figs are yellow initially and measure across. Ripening to red in colour, they are tipped with a small nipple and on a stalk. Fruits ripen throughout the year, although more so in spring and summer. Some trees have ripe and unripe fruit at the same time.
It closely resembles its relative, the Moreton Bay fig (F. macrophylla). Having similar ranges in the wild, they are often confused.
The smaller leaves, shorter fruit stalks, and rusty colour of the undersides of the leaves of F. rubiginosa are the easiest distinguishing features. It is also confused with the small-leaved fig (F. obliqua), the syconia of which are smaller, measuring 4–12 mm long and 4–11 mm in diameter, compared with 7–17 mm long and 8–17 mm diameter for F. rubiginosa.
Distribution and habitat
Ficus rubiginosas range spans the entire eastern coastline of Australia, from the top of the Cape York Peninsula in north Queensland to the vicinity of Bega on the south coast of New South Wales. The range extends westwards to Porcupine Gorge National Park in Queensland and the far western plains in New South Wales. F. rubiginosa f. rubiginosa and F. rubiginosa f. glabrescens are found over most of the range, though the latter does not occur south past the New South Wales-Queensland border region. Lithophytic, hemiepiphytic, and tree forms can be found together in local populations of plants.
F. rubiginosa is found in rainforest, rainforest margins, gullies, riverbank habitat, vine thickets, and rocky hillsides. It is found on limestone outcrops in Kanangra-Boyd National Park. Fig seedlings often grow from cracks in stone where seeds have been lodged, in locations such as cliffs and rock faces in natural environments, or in brickwork on buildings and elsewhere in the urban environment. The soils it grows on are often well-drained and low in nutrients. They are derived from sandstone, quartzite, and basalt. In the Sydney region, F. rubiginosa grows from sea level to 1000 m (3500 ft) altitude, in areas with an average yearly rainfall of . F. rubiginosa is largely sympatric with F. obliqua, though its range extends further west into dryer regions than the latter species.
Outside its native range, F. rubiginosa has naturalised to some degree in urban Melbourne and Adelaide in Australia, as well as New Zealand, Hawaii and California, and Mediterranean Europe. F. rubiginosa has been planted widely in Malta since the early 1990s but has not been observed to fruit.
Ecology
The fruit is consumed by many bird species including the rose-crowned fruit dove (Ptilinopus regina), wompoo fruit dove (P. magnificus), wonga pigeon (Leucosarcia melanoleuca), topknot pigeon (Lopholaimus antarcticus), Pacific koel (Eudynamys orientalis), Australasian swamphen (Porphyrio melanotus), Australian king parrot (Alisterus scapularis), Australasian figbird (Sphecotheres vieilloti), green catbird (Ailuroedus crassirostris), regent bowerbird (Sericulus chrysocephalus), satin bowerbird (Ptilonorhynchus violaceus) and pied currawong (Strepera graculina), as well as the mammalian grey-headed flying fox (Pteropus poliocephalus), and spectacled flying fox (Pteropus conspicillatus). It is one of several plant species used as food by the endangered Coxen's fig parrot. Many fruits drop onto the ground around the tree, though others are dispersed by animals that eat them.
The thrips species Gynaikothrips australis feeds on the underside of new leaves of F. rubiginosa, as well as F. obliqua and F. macrophylla. As plant cells die, nearby cells are induced into forming meristem tissue, and a gall results and the leaves become distorted and curl over. The thrips begin feeding when the tree has flushes of new growth, and live for around six weeks. At other times, thrips reside on old leaves without feeding. The species pupates sheltered in the bark. The thrips remain in the galls at night, wander about in the daytime and return in the evening, possibly to different galls about the tree. Psyllids have almost defoliated trees in the Royal Botanic Gardens in Sydney in spring.
P. imperialis crossed the waters between Australia and New Zealand some time between 1960 and 1972, and seedlings of the previously infertile trees of F. rubiginosa began appearing in brick and stone walls, and on other trees, particularly in parks and gardens around Auckland. They have been recorded as far south as Napier. P. imperialis has been transported to Hawaii, California, and Israel, where it has been observed to pollinate its host.
They can live to 100 years or more and have been known to resprout after bushfire, bearing fruit within three years.
Other life in the syconia
As with many other Ficus species, the community of wasps inside the figs of F. rubiginosa is made up mostly of pollinator wasps. These develop deep inside the syconium, presumably protected there from parasites. Also present are much smaller numbers of other wasp species, which do not pollinate the fig. At least fourteen species have been recorded, of which four—two each belonging to the genera Sycoscapter and Philotrypesis—are common while others are rare. Investigation of F. rubiginosa syconia found that the fig seeds and parasitic wasps develop closer to the wall of the syconium. The wasps of the genera Sycoscapter and Philotrypesis are parasitic and are around the same size as the pollinator species. Their larvae are thought to feed on the larvae of the pollinator wasp. Male Sycoscapter and Philotrypesis wasps fight other males of the same species when they encounter each other in a F. rubiginosa fig. Several genera of uncommon larger wasp species enter the immature figs before other wasps and induce galls, which may impact on numbers of pollinator wasps in the fig later. An example of this is Pseudidarnes minerva, a metallic green wasp species.
Nematodes of the genus Schistonchus are found in the syconia (and the pollinator wasps) of many species of fig, with F. rubiginosa hosting two species. They appear to be less species-specific than wasps. S. altermacrophylla is generally associated with F. rubiginosa though it has been recorded on several other fig species.
Cultivation
Ficus rubiginosa was first cultivated in the United Kingdom in 1789, where it is grown in glasshouses. It is commonly used as a large ornamental tree in eastern Australia, in the North Island of New Zealand, and also in Hawaii and California, where it is also listed as an invasive species in some areas. It is useful as a shade tree in public parks and on golf courses. Not as prodigious as other figs, F. rubiginosa is suited to slightly more confined areas, such as lining car parks or suburban streets. However, surface roots can be large and intrusive and the thin bark readily damaged when struck. Tolerant of acid or alkaline soils, it is hardy to US Hardiness Zones 10B and 11, reaching high in 30 years. Planting trees apart will eventually result in a continuous canopy. The trees are of great value in providing fruit for birds and mammals, though drop large quantities of fruit and leaves, leaving a mess underfoot.
In a brief description, William Guilfoyle recorded a variegated fig from New South Wales "12–15 ft high" in 1911 as F. rubiginosa variety variegata. A variegated form is in cultivation on Australia's east coast, and in the United States. It is a chimera lacking in chlorophyll in the second layer of the leaf meristem. The leaves have an irregular central green patch along the midvein with irregular yellow and green elsewhere. Leaves that grow in winter generally have larger green patches than those that do in summer. The chimera is unstable, and branches of all-green growth appear sporadically.
Despite the relatively large size of the leaves, it is popular for bonsai work as it is highly forgiving to work with and hard to kill; the leaves reduce readily by leaf-pruning in early summer. Described as the best tree for a beginner to work with, it is one of the most frequently used native species in Australia. Its bark remains smooth, and does not attain a rugged, aged appearance. Known as "Little Ruby", a narrow-leaved form with its origins somewhere north of Sydney is also seen in cultivation.
F. rubiginosa is also suited for use as a houseplant in low, medium or brightly lit spaces, although a variegated form requires brighter light. It has gained the Royal Horticultural Society's Award of Garden Merit. It is easily propagated by cuttings or aerial layering.
The light-coloured wood is soft and brittle. Lightweight, it has some value in the making of such items as toys and small boxes.
See also
Ficus macrophylla
Notes
References
External links
Jared Bernard et al.: New Species Assemblages Disrupt Obligatory Mutualisms Between Figs and Their Pollinators. In: Front. Ecol. Evol., 19 November 2020. doi:10.3389/fevo.2020.564653. See also:
Jared Bernard: Figs show that nonnative species can invade ecosystems by forming unexpected partnerships. On: The Conversation. 19 January 2021. Also on Sciencealert
Rubiginosa
Rosales of Australia
Trees of Australia
Flora of New South Wales
Flora of Queensland
Rubiginosa
Plants used in bonsai
Garden plants of Australia
Ornamental trees
Lithophytes
Least concern flora of Australia | Ficus rubiginosa | [
"Biology"
] | 3,546 | [
"Lithophytes",
"Plants"
] |
362,348 | https://en.wikipedia.org/wiki/Terahertz%20radiation | Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the International Telecommunication Union-designated band of frequencies from 0.3 to 3 terahertz (THz), although the upper boundary is somewhat arbitrary and is considered by some sources as 30 THz. One terahertz is 1012 Hz or 1,000 GHz. Wavelengths of radiation in the terahertz band correspondingly range from 1 mm to 0.1 mm = 100 μm. Because terahertz radiation begins at a wavelength of around 1 millimeter and proceeds into shorter wavelengths, it is sometimes known as the submillimeter band, and its radiation as submillimeter waves, especially in astronomy. This band of electromagnetic radiation lies within the transition region between microwave and far infrared, and can be regarded as either.
Compared to lower radio frequencies, terahertz radiation is strongly absorbed by the gases of the atmosphere, and in air most of the energy is attenuated within a few meters, so it is not practical for long distance terrestrial radio communication. It can penetrate thin layers of materials but is blocked by thicker objects. THz beams transmitted through materials can be used for material characterization, layer inspection, relief measurement, and as a lower-energy alternative to X-rays for producing high resolution images of the interior of solid objects.
Terahertz radiation occupies a middle ground where the ranges of microwaves and infrared light waves overlap, known as the "terahertz gap"; it is called a "gap" because the technology for its generation and manipulation is still in its infancy. The generation and modulation of electromagnetic waves in this frequency range ceases to be possible by the conventional electronic devices used to generate radio waves and microwaves, requiring the development of new devices and techniques.
Description
Terahertz radiation falls in between infrared radiation and microwave radiation in the electromagnetic spectrum, and it shares some properties with each of these. Terahertz radiation travels in a line of sight and is non-ionizing. Like microwaves, terahertz radiation can penetrate a wide variety of non-conducting materials; clothing, paper, cardboard, wood, masonry, plastic and ceramics. The penetration depth is typically less than that of microwave radiation. Like infrared, terahertz radiation has limited penetration through fog and clouds and cannot penetrate liquid water or metal. Terahertz radiation can penetrate some distance through body tissue like x-rays, but unlike them is non-ionizing, so it is of interest as a replacement for medical X-rays. Due to its longer wavelength, images made using terahertz waves have lower resolution than X-rays and need to be enhanced (see figure at right).
The earth's atmosphere is a strong absorber of terahertz radiation, so the range of terahertz radiation in air is limited to tens of meters, making it unsuitable for long-distance communications. However, at distances of ~10 meters the band may still allow many useful applications in imaging and construction of high bandwidth wireless networking systems, especially indoor systems. In addition, producing and detecting coherent terahertz radiation remains technically challenging, though inexpensive commercial sources now exist in the 0.3–1.0 THz range (the lower part of the spectrum), including gyrotrons, backward wave oscillators, and resonant-tunneling diodes. Due to the small energy of THz photons, current THz devices require low temperature during operation to suppress environmental noise. Tremendous efforts thus have been put into THz research to improve the operation temperature, using different strategies such as optomechanical meta-devices.
Sources
Natural
Terahertz radiation is emitted as part of the black-body radiation from anything with a temperature greater than about 2 kelvin. While this thermal emission is very weak, observations at these frequencies are important for characterizing cold 10–20 K cosmic dust in interstellar clouds in the Milky Way galaxy, and in distant starburst galaxies.
Telescopes operating in this band include the James Clerk Maxwell Telescope, the Caltech Submillimeter Observatory and the Submillimeter Array at the Mauna Kea Observatory in Hawaii, the BLAST balloon borne telescope, the Herschel Space Observatory, the Heinrich Hertz Submillimeter Telescope at the Mount Graham International Observatory in Arizona, and at the recently built Atacama Large Millimeter Array. Due to Earth's atmospheric absorption spectrum, the opacity of the atmosphere to submillimeter radiation restricts these observatories to very high altitude sites, or to space.
Artificial
, viable sources of terahertz radiation are the gyrotron, the backward wave oscillator ("BWO"), the molecule gas far-infrared laser, Schottky-diode multipliers, varactor (varicap) multipliers, quantum-cascade laser, the free-electron laser, synchrotron light sources, photomixing sources, single-cycle or pulsed sources used in terahertz time-domain spectroscopy such as photoconductive, surface field, photo-Dember and optical rectification emitters, and electronic oscillators based on resonant tunneling diodes have been shown to operate up to 1.98 THz.
There have also been solid-state sources of millimeter and submillimeter waves for many years. AB Millimeter in Paris, for instance, produces a system that covers the entire range from 8 GHz to 1,000 GHz with solid state sources and detectors. Nowadays, most time-domain work is done via ultrafast lasers.
In mid-2007, scientists at the U.S. Department of Energy's Argonne National Laboratory, along with collaborators in Turkey and Japan, announced the creation of a compact device that could lead to portable, battery-operated terahertz radiation sources. The device uses high-temperature superconducting crystals, grown at the University of Tsukuba in Japan. These crystals comprise stacks of Josephson junctions, which exhibit a property known as the Josephson effect: when external voltage is applied, alternating current flows across the junctions at a frequency proportional to the voltage. This alternating current induces an electromagnetic field. A small voltage (around two millivolts per junction) can induce frequencies in the terahertz range.
In 2008, engineers at Harvard University achieved room temperature emission of several hundred nanowatts of coherent terahertz radiation using a semiconductor source. THz radiation was generated by nonlinear mixing of two modes in a mid-infrared quantum cascade laser. Previous sources had required cryogenic cooling, which greatly limited their use in everyday applications.
In 2009, it was discovered that the act of unpeeling adhesive tape generates non-polarized terahertz radiation, with a narrow peak at 2 THz and a broader peak at 18 THz. The mechanism of its creation is tribocharging of the adhesive tape and subsequent discharge; this was hypothesized to involve bremsstrahlung with absorption or energy density focusing during dielectric breakdown of a gas.
In 2013, researchers at Georgia Institute of Technology's Broadband Wireless Networking Laboratory and the Polytechnic University of Catalonia developed a method to create a graphene antenna: an antenna that would be shaped into graphene strips from 10 to 100 nanometers wide and one micrometer long. Such an antenna could be used to emit radio waves in the terahertz frequency range.
Terahertz gap
In engineering, the terahertz gap is a frequency band in the THz region for which practical technologies for generating and detecting the radiation do not exist. It is defined as 0.1 to 10 THz (wavelengths of 3 mm to 30 μm) although the upper boundary is somewhat arbitrary and is considered by some sources as 30 THz (a wavelength of 10 μm). Currently, at frequencies within this range, useful power generation and receiver technologies are inefficient and unfeasible.
Mass production of devices in this range and operation at room temperature (at which energy kT is equal to the energy of a photon with a frequency of 6.2 THz) are mostly impractical. This leaves a gap between mature microwave technologies in the highest frequencies of the radio spectrum and the well-developed optical engineering of infrared detectors in their lowest frequencies. This radiation is mostly used in small-scale, specialized applications such as submillimetre astronomy. Research that attempts to resolve this issue has been conducted since the late 20th century.
In 2024, an experiment has been published by German researchers where a TDLAS experiment at 4.75 THz has been performed in "infrared quality" with an uncooled pyroelectric receiver while the THz source has been a cw DFB-QC-Laser operated at 43.3 K and laser currents between 480 mA and 600 mA.
Closure of the terahertz gap
Most vacuum electronic devices that are used for microwave generation can be modified to operate at terahertz frequencies, including the magnetron, gyrotron, synchrotron, and free-electron laser. Similarly, microwave detectors such as the tunnel diode have been re-engineered to detect at terahertz and infrared frequencies as well. However, many of these devices are in prototype form, are not compact, or exist at university or government research labs, without the benefit of cost savings due to mass production.
Research
Molecular biology
Terahertz radiation has comparable frequencies to the motion of biomolecular systems in the course of their function (a frequency 1THz is equivalent to a timescale of 1 picosecond, therefore in particular the range of hundreds of GHz up to low numbers of THz is comparable to biomolecular relaxation timescales of a few ps to a few ns). Modulation of biological and also neurological function is therefore possible using radiation in the range hundreds of GHz up to a few THz at relatively low energies (without significant heating or ionisation) achieving either beneficial or harmful effects.
Medical imaging
Unlike X-rays, terahertz radiation is not ionizing radiation and its low photon energies in general do not damage living tissues and DNA. Some frequencies of terahertz radiation can penetrate several millimeters of tissue with low water content (e.g., fatty tissue) and reflect back. Terahertz radiation can also detect differences in water content and density of a tissue. Such methods could allow effective detection of epithelial cancer with an imaging system that is safe, non-invasive, and painless. In response to the demand for COVID-19 screening terahertz spectroscopy and imaging has been proposed as a rapid screening tool.
The first images generated using terahertz radiation date from the 1960s; however, in 1995 images generated using terahertz time-domain spectroscopy generated a great deal of interest.
Some frequencies of terahertz radiation can be used for 3D imaging of teeth and may be more accurate than conventional X-ray imaging in dentistry.
Security
Terahertz radiation can penetrate fabrics and plastics, so it can be used in surveillance, such as security screening, to uncover concealed weapons on a person, remotely. This is of particular interest because many materials of interest have unique spectral "fingerprints" in the terahertz range. This offers the possibility to combine spectral identification with imaging. In 2002, the European Space Agency (ESA) Star Tiger team, based at the Rutherford Appleton Laboratory (Oxfordshire, UK), produced the first passive terahertz image of a hand. By 2004, ThruVision Ltd, a spin-out from the Council for the Central Laboratory of the Research Councils (CCLRC) Rutherford Appleton Laboratory, had demonstrated the world's first compact THz camera for security screening applications. The prototype system successfully imaged guns and explosives concealed under clothing. Passive detection of terahertz signatures avoid the bodily privacy concerns of other detection by being targeted to a very specific range of materials and objects.
In January 2013, the NYPD announced plans to experiment with the new technology to detect concealed weapons, prompting Miami blogger and privacy activist Jonathan Corbett to file a lawsuit against the department in Manhattan federal court that same month, challenging such use: "For thousands of years, humans have used clothing to protect their modesty and have quite reasonably held the expectation of privacy for anything inside of their clothing, since no human is able to see through them." He sought a court order to prohibit using the technology without reasonable suspicion or probable cause. By early 2017, the department said it had no intention of ever using the sensors given to them by the federal government.
Scientific use and imaging
In addition to its current use in submillimetre astronomy, terahertz radiation spectroscopy could provide new sources of information for chemistry and biochemistry.
Recently developed methods of THz time-domain spectroscopy (THz TDS) and THz tomography have been shown to be able to image samples that are opaque in the visible and near-infrared regions of the spectrum. The utility of THz-TDS is limited when the sample is very thin, or has a low absorbance, since it is very difficult to distinguish changes in the THz pulse caused by the sample from those caused by long-term fluctuations in the driving laser source or experiment. However, THz-TDS produces radiation that is both coherent and spectrally broad, so such images can contain far more information than a conventional image formed with a single-frequency source.
Submillimeter waves are used in physics to study materials in high magnetic fields, since at high fields (over about 11 tesla), the electron spin Larmor frequencies are in the submillimeter band. Many high-magnetic field laboratories perform these high-frequency EPR experiments, such as the National High Magnetic Field Laboratory (NHMFL) in Florida.
Terahertz radiation could let art historians see murals hidden beneath coats of plaster or paint in centuries-old buildings, without harming the artwork.
In additional, THz imaging has been done with lens antennas to capture radio image of the object.
Particle accelerators
New types of particle accelerators that could achieve multi Giga-electron volts per metre (GeV/m) accelerating gradients are of utmost importance to reduce the size and cost of future generations of high energy colliders as well as provide a widespread availability of compact accelerator technology to smaller laboratories around the world. Gradients in the order of 100 MeV/m have been achieved by conventional techniques and are limited by RF-induced plasma breakdown. Beam driven dielectric wakefield accelerators (DWAs) typically operate in the Terahertz frequency range, which pushes the plasma breakdown threshold for surface electric fields into the multi-GV/m range. DWA technique allows to accommodate a significant amount of charge per bunch, and gives an access to conventional fabrication techniques for the accelerating structures. To date 0.3 GeV/m accelerating and 1.3 GeV/m decelerating gradients have been achieved using a dielectric lined waveguide with sub-millimetre transverse aperture.
An accelerating gradient larger than 1 GeV/m, can potentially be produced by the Cherenkov Smith-Purcell radiative mechanism in a dielectric capillary with a variable inner radius. When an electron bunch propagates through the capillary, its self-field interacts with the dielectric material and produces wakefields that propagate inside the material at the Cherenkov angle. The wakefields are slowed down below the speed of light, as the relative dielectric permittivity of the material is larger than 1. The radiation is then reflected from the capillary's metallic boundary and diffracted back into the vacuum region, producing high accelerating fields on the capillary axis with a distinct frequency signature. In presence of a periodic boundary the Smith-Purcell radiation imposes frequency dispersion.
A preliminary study with corrugated capillaries has shown some modification to the spectral content and amplitude of the generated wakefields, but the possibility of using Smith-Purcell effect in DWA is still under consideration.
Communication
The high atmospheric absorption of terahertz waves limits the range of communication using existing transmitters and antennas to tens of meters. However, the huge unallocated bandwidth available in the band (ten times the bandwidth of the millimeter wave band, 100 times that of the SHF microwave band) makes it very attractive for future data transmission and networking use. There are tremendous difficulties to extending the range of THz communication through the atmosphere, but the world telecommunications industry is funding much research into overcoming those limitations. One promising application area is the 6G cellphone and wireless standard, which will supersede the current 5G standard around 2030.
For a given antenna aperture, the gain of directive antennas scales with the square of frequency, while for low power transmitters the power efficiency is independent of bandwidth. So the consumption factor theory of communication links indicates that, contrary to conventional engineering wisdom, for a fixed aperture it is more efficient in bits per second per watt to use higher frequencies in the millimeter wave and terahertz range. Small directive antennas a few centimeters in diameter can produce very narrow 'pencil' beams of THz radiation, and phased arrays of multiple antennas could concentrate virtually all the power output on the receiving antenna, allowing communication at longer distances.
In May 2012, a team of researchers from the Tokyo Institute of Technology published in Electronics Letters that it had set a new record for wireless data transmission by using T-rays and proposed they be used as bandwidth for data transmission in the future. The team's proof of concept device used a resonant tunneling diode (RTD) negative resistance oscillator to produce waves in the terahertz band. With this RTD, the researchers sent a signal at 542 GHz, resulting in a data transfer rate of 3 Gigabits per second. It doubled the record for data transmission rate set the previous November. The study suggested that Wi-Fi using the system would be limited to approximately , but could allow data transmission at up to 100 Gbit/s. In 2011, Japanese electronic parts maker Rohm and a research team at Osaka University produced a chip capable of transmitting 1.5 Gbit/s using terahertz radiation.
Potential uses exist in high-altitude telecommunications, above altitudes where water vapor causes signal absorption: aircraft to satellite, or satellite to satellite.
Amateur radio
A number of administrations permit amateur radio experimentation within the 275–3,000 GHz range or at even higher frequencies on a national basis, under license conditions that are usually based on RR5.565 of the ITU Radio Regulations. Amateur radio operators utilizing submillimeter frequencies often attempt to set two-way communication distance records. In the United States, WA1ZMS and W4WWQ set a record of on 403 GHz using CW (Morse code) on 21 December 2004. In Australia, at 30 THz a distance of was achieved by stations VK3CV and VK3LN on 8 November 2020.
Manufacturing
Many possible uses of terahertz sensing and imaging are proposed in manufacturing, quality control, and process monitoring. These in general exploit the traits of plastics and cardboard being transparent to terahertz radiation, making it possible to inspect packaged goods. The first imaging system based on optoelectronic terahertz time-domain spectroscopy were developed in 1995 by researchers from AT&T Bell Laboratories and was used for producing a transmission image of a packaged electronic chip. This system used pulsed laser beams with duration in range of picoseconds. Since then commonly used commercial/ research terahertz imaging systems have used pulsed lasers to generate terahertz images. The image can be developed based on either the attenuation or phase delay of the transmitted terahertz pulse.
Since the beam is scattered more at the edges and also different materials have different absorption coefficients, the images based on attenuation indicates edges and different materials inside of objects. This approach is similar to X-ray transmission imaging, where images are developed based on attenuation of the transmitted beam.
In the second approach, terahertz images are developed based on the time delay of the received pulse. In this approach, thicker parts of the objects are well recognized as the thicker parts cause more time delay of the pulse. Energy of the laser spots are distributed by a Gaussian function. The geometry and behavior of Gaussian beam in the Fraunhofer region imply that the electromagnetic beams diverge more as the frequencies of the beams decrease and thus the resolution decreases. This implies that terahertz imaging systems have higher resolution than scanning acoustic microscope (SAM) but lower resolution than X-ray imaging systems. Although terahertz can be used for inspection of packaged objects, it suffers from low resolution for fine inspections. X-ray image and terahertz images of an electronic chip are brought in the figure on the right. Obviously the resolution of X-ray is higher than terahertz image, but X-ray is ionizing and can be impose harmful effects on certain objects such as semiconductors and live tissues.
To overcome low resolution of the terahertz systems near-field terahertz imaging systems are under development. In nearfield imaging the detector needs to be located very close to the surface of the plane and thus imaging of the thick packaged objects may not be feasible. In another attempt to increase the resolution, laser beams with frequencies higher than terahertz are used to excite the p-n junctions in semiconductor objects, the excited junctions generate terahertz radiation as a result as long as their contacts are unbroken and in this way damaged devices can be detected. In this approach, since the absorption increases exponentially with the frequency, again inspection of the thick packaged semiconductors may not be doable. Consequently, a tradeoff between the achievable resolution and the thickness of the penetration of the beam in the packaging material should be considered.
THz gap research
Ongoing investigation has resulted in improved emitters (sources) and detectors, and research in this area has intensified. However, drawbacks remain that include the substantial size of emitters, incompatible frequency ranges, and undesirable operating temperatures, as well as component, device, and detector requirements that are somewhere between solid state electronics and photonic technologies.
Free-electron lasers can generate a wide range of stimulated emission of electromagnetic radiation from microwaves, through terahertz radiation to X-ray. However, they are bulky, expensive and not suitable for applications that require critical timing (such as wireless communications). Other sources of terahertz radiation which are actively being researched include solid state oscillators (through frequency multiplication), backward wave oscillators (BWOs), quantum cascade lasers, and gyrotrons.
Safety
The terahertz region is between the radio frequency region and the laser optical region. Both the IEEE C95.1–2005 RF safety standard and the ANSI Z136.1–2007 Laser safety standard have limits into the terahertz region, but both safety limits are based on extrapolation. It is expected that effects on biological tissues are thermal in nature and, therefore, predictable by conventional thermal models . Research is underway to collect data to populate this region of the spectrum and validate safety limits.
A theoretical study published in 2010 and conducted by Alexandrov et al at the Center for Nonlinear Studies at Los Alamos National Laboratory in New Mexico created mathematical models predicting how terahertz radiation would interact with double-stranded DNA, showing that, even though involved forces seem to be tiny, nonlinear resonances (although much less likely to form than less-powerful common resonances) could allow terahertz waves to "unzip double-stranded DNA, creating bubbles in the double strand that could significantly interfere with processes such as gene expression and DNA replication". Experimental verification of this simulation was not done. Swanson's 2010 theoretical treatment of the Alexandrov study concludes that the DNA bubbles do not occur under reasonable physical assumptions or if the effects of temperature are taken into account. A bibliographical study published in 2003 reported that T-ray intensity drops to less than 1% in the first 500 μm of skin but stressed that "there is currently very little information about the optical properties of human tissue at terahertz frequencies".
See also
Far-infrared laser
Full body scanner
Heterojunction bipolar transistor
High-electron-mobility transistor (HEMT)
Picarin
Terahertz time-domain spectroscopy
Microwave analog signal processing
References
Further reading
External links
Electromagnetic spectrum
Terahertz technology | Terahertz radiation | [
"Physics"
] | 5,117 | [
"Spectrum (physical sciences)",
"Electromagnetic spectrum",
"Terahertz technology"
] |
362,400 | https://en.wikipedia.org/wiki/Separable%20polynomial | In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial.
This concept is closely related to square-free polynomial. If K is a perfect field then the two concepts coincide. In general, P(X) is separable if and only if it is square-free over any field that contains K,
which holds if and only if P(X) is coprime to its formal derivative D P(X).
Older definition
In an older definition, P(X) was considered separable if each of its irreducible factors in K[X] is separable in the modern definition. In this definition, separability depended on the field K; for example, any polynomial over a perfect field would have been considered separable. This definition, although it can be convenient for Galois theory, is no longer in use.
Separable field extensions
Separable polynomials are used to define separable extensions: A field extension is a separable extension if and only if for every in which is algebraic over , the minimal polynomial of over is a separable polynomial.
Inseparable extensions (that is, extensions which are not separable) may occur only in positive characteristic.
The criterion above leads to the quick conclusion that if P is irreducible and not separable, then D P(X) = 0.
Thus we must have
P(X) = Q(X p)
for some polynomial Q over K, where the prime number p is the characteristic.
With this clue we can construct an example:
P(X) = X p − T
with K the field of rational functions in the indeterminate T over the finite field with p elements. Here one can prove directly that P(X) is irreducible and not separable. This is actually a typical example of why inseparability matters; in geometric terms P represents the mapping on the projective line over the finite field, taking co-ordinates to their pth power. Such mappings are fundamental to the algebraic geometry of finite fields. Put another way, there are coverings in that setting that cannot be 'seen' by Galois theory. (See Radical morphism for a higher-level discussion.)
If L is the field extension
K(T 1/p),
in other words the splitting field of P, then L/K is an example of a purely inseparable field extension. It is of degree p, but has no automorphism fixing K, other than the identity, because T 1/p is the unique root of P. This shows directly that Galois theory must here break down. A field such that there are no such extensions is called perfect. That finite fields are perfect follows a posteriori from their known structure.
One can show that the tensor product of fields of L with itself over K for this example has nilpotent elements that are non-zero. This is another manifestation of inseparability: that is, the tensor product operation on fields need not produce a ring that is a product of fields (so, not a commutative semisimple ring).
If P(x) is separable, and its roots form a group (a subgroup of the field K), then P(x) is an additive polynomial.
Applications in Galois theory
Separable polynomials occur frequently in Galois theory.
For example, let P be an irreducible polynomial with integer coefficients and p be a prime number which does not divide the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained by reducing modulo p the coefficients of P. Then, if Q is separable (which is the case for every p but a finite number) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P.
Another example: P being as above, a resolvent R for a group G is a polynomial whose coefficients are polynomials in the coefficients of P, which provides some information on the Galois group of P. More precisely, if R is separable and has a rational root then the Galois group of P is contained in G. For example, if D is the discriminant of P then is a resolvent for the alternating group. This resolvent is always separable (assuming the characteristic is not 2) if P is irreducible, but most resolvents are not always separable.
See also
Frobenius endomorphism
References
Field (mathematics)
Polynomials | Separable polynomial | [
"Mathematics"
] | 971 | [
"Polynomials",
"Algebra"
] |
362,464 | https://en.wikipedia.org/wiki/Genentech | Genentech, Inc. is an American biotechnology corporation headquartered in South San Francisco, California, wholly owned by the Swiss multinational pharmaceutical company, the Roche Group. It became an independent subsidiary of Roche in 2009. Genentech Research and Early Development operates as an independent center within Roche. Historically, the company is regarded as the world's first biotechnology company.
As of July 2021, Genentech employed 13,539 people.
History
The company was founded in 1976 by venture capitalist Robert A. Swanson and biochemist Herbert Boyer. Boyer is considered to be a pioneer in the field of recombinant DNA technology. In 1973, Boyer and his colleague Stanley Norman Cohen demonstrated that restriction enzymes could be used as "scissors" to cut DNA fragments of interest from one source, to be ligated into a similarly cut plasmid vector. While Cohen returned to the laboratory in academia, Swanson contacted Boyer to found the company. Boyer worked with Arthur Riggs and Keiichi Itakura from the Beckman Research Institute, and the group became the first to successfully express a human gene in bacteria when they produced the hormone somatostatin in 1977. David Goeddel and Dennis Kleid were then added to the group, and contributed to its success with synthetic human insulin in 1978.
In 1990 F. Hoffmann-La Roche AG acquired a majority stake in Genentech.
In 2006 Genentech acquired Tanox in its first acquisition deal. Tanox had started developing Xolair and development was completed in collaboration with Novartis and Genentech; the acquisition allowed Genentech to keep more of the revenue.
In March 2009 Roche acquired Genentech by buying shares it didn't already control for approximately $46.8 billion.
In July 2014, Genentech/Roche acquired Seragon for its pipeline of small-molecule cancer drug candidates for $725 million cash upfront, with an additional $1 billion of payments dependent on successful development of products in Seragon's pipeline.
Research
Genentech is a pioneering research-driven biotechnology company that has continued to conduct R&D internally as well as through collaborations.
Genentech's research collaborations include:
In 2008 Genentech entered into a collaboration with Roche and its subsidiary GlycArt to develop obinutuzumab.
In February 2010 Genentech entered into a collaboration with University of California, San Francisco after having worked with them in about fifteen other collaborations, this time to collaborate on small molecule drug discovery in neurology.
In October 2014 Genentech paid $150M upfront to collaborate with Iowa-based NewLink Genetics on checkpoint inhibitors.
In June 2015 it entered into a wide-ranging partnership with The Data Incubator to help train and hire the next generation of data scientists at the company.
In January 2015 it signed a $60M deal with 23andMe that gave Genentech access to the genomic and patient-reported data held by 23andMe.
In October 2015 it started a collaboration with Nimbus Therapeutics to develop leads from Nimbus' in silico drug discovery platform.
In June 2016 Genentech partnered Epizyme to conduct clinical trials exploring whether Epizyme's EZH2 inhibitor tazemetostat would be synergistic with Genentech's atezolizumab.
In August 2016, the company began a collaboration with Carmot Therapeutics in which Carmot will discover new candidates and Genentech will develop them.
In September 2016 Genentech partnered with the Israeli company BioLineRx on a checkpoint inhibitor that Genentech intended to pair with its own atezolizumab.
Facilities
Genentech's corporate headquarters are in South San Francisco, California (), with additional manufacturing facilities in Vacaville, California; Oceanside, California; and Hillsboro, Oregon. In March 2024, it was announced the Swiss pharmaceutical company, Lonza had acquired the Vacaville site from parent-company, Roche for $1.2 billion.
In December 2006, Genentech sold its Porriño, Spain, facility to Lonza and acquired an exclusive right to purchase Lonza's mammalian cell culture manufacturing facility under construction in Singapore. In June 2007, Genentech began the construction and development of an E. coli manufacturing facility, also in Singapore, for the worldwide production of Lucentis (ranibizumab injection) bulk drug substance.
In 2023, the company announced plans to close down its manufacturing facility in South San Francisco, while expanding its manufacturing capabilities in Oceanside.
Public-private engagement
Political lobbying
Genentech is a donor to the Center for Health Care Strategies, a non-governmental organization that lobbies the United States Government on issues related to Medicaid.
Genentech Inc Political Action Committee
Genentech Inc Political Action Committee is a U.S. Federal Political Action Committee (PAC), created to "aggregate contributions from members or employees and their families to donate to candidates for federal office".
Controversy
Disputes
In November 1999, Genentech agreed to pay the University of California, San Francisco $200 million to settle a nine-year-old patent dispute. In 1990, UCSF sued Genentech for $400 million in compensation for alleged theft of technology developed at the university and covered by a 1982 patent. Genentech claimed that they developed Protropin (recombinant somatotropin/human growth hormone), independently of UCSF. A jury ruled that the university's patent was valid in July 1999, but wasn't able to decide whether Protropin was based upon UCSF research or not. Protropin, a drug used to treat dwarfism, was Genentech's first marketed drug and its $2 billion in sales has contributed greatly to its position as an industry leader. The settlement was to be divided as follows: $30 million to the University of California General Fund, $85 million to the three inventors and two collaborating scientists, $50 million towards a new teaching and research campus for UCSF, and $35 million to support university-wide research.
In 2009, The New York Times reported that Genentech's talking points on health care reform appeared verbatim in the official statements of several Members of Congress during the national health care reform debate. Two U.S. Representatives, Joe Wilson and Blaine Luetkemeyer, both issued the same written statements: "One of the reasons I have long supported the U.S. biotechnology industry is that it is a homegrown success story that has been an engine of job creation in this country. Unfortunately, many of the largest companies that would seek to enter the biosimilar market have made their money by outsourcing their research to foreign countries like India." The statement was originally drafted by lobbyists for Genentech.
Products timeline
1982: Synthetic "human" insulin approved by the U.S. Food and Drug Administration (FDA), partnered with insulin manufacturer Eli Lilly and Company, who shepherded the product through the FDA approval process. The product (Humulin) was licensed to and manufactured by Lilly, and was the first-ever approved genetically engineered human therapeutic.
1985: Protropin (somatrem): Supplementary growth hormone for children with growth hormone deficiency (ceased manufacturing 2004).
1987: Activase (alteplase): A recombinant tissue plasminogen activator (tPa) used to dissolve blood clots in patients with acute myocardial infarction. Also used to treat non-hemorrhagic stroke.
1990: Actimmune (interferon gamma 1b): Treatment of chronic granulomatous disease (licensed to Intermune).
1993: Nutropin (recombinant somatropin): Growth hormone for children and adults for treatment before kidney transplant due to chronic kidney disease.
1993: Pulmozyme (dornase alfa): Inhalation treatment for children and young adults with cystic fibrosis—recombinant DNAse.
1997: Rituxan (rituximab): Treatment for specific kinds of non-Hodgkin's lymphomas. In 2006, also approved for rheumatoid arthritis.
1998: Herceptin (trastuzumab): Treatment for metastatic breast cancer patients with tumors that overexpress the HER2 gene. Recently approved for adjuvant therapy for breast cancer. FDA also recently approved Trastuzumab for metastatic gastric cancer with HER2 receptor site positive.
2000: TNKase (tenecteplase): "Clot-busting" drug to treat acute myocardial infarction.
2003: Xolair (omalizumab): Subcutaneous injection for moderate to severe persistent asthma.
2003: Raptiva (efalizumab): Antibody designed to block the activation and reactivation of T cells that lead to the development of psoriasis. Developed in partnership with XOMA. In 2009, voluntary U.S. market withdrawal after reports of progressive multifocal leukoencephalopathy.
2004: Avastin (bevacizumab): Anti-VEGF monoclonal antibody for the treatment of metastatic cancer of the colon or rectum. In 2006, also approved for locally advanced, recurrent or metastatic non-small cell lung cancer. In 2008, accelerated approval was granted for Avastin in combination with chemotherapy for previously untreated advanced HER2-negative breast cancer. In 2009, Avastin gained its fifth approval for treatment of glioblastoma multiforme, and sixth approval for the treatment of metastatic renal cell carcinoma. It was most publicized for its approval in advanced breast cancer treatment, but the FDA approval for breast cancer treatment was subsequently revoked in November 2011.
2004: Tarceva (erlotinib): Treatment for patients with locally advanced or metastatic non-small cell lung cancer, and pancreatic cancer.
2006: Lucentis (ranibizumab injection): Treatment of neovascular (wet) age-related macular degeneration (AMD). The FDA approved LUCENTIS after a Priority Review (six-month). Genentech started shipping product on June 30, 2006, the day the product was approved.
2010: Actemra (tocilizumab): The first interleukin-6 (IL-6) receptor-inhibiting monoclonal antibody approved to treat rheumatoid arthritis.
2011: Zelboraf (vemurafenib): For the treatment of metastatic melanoma caused by BRAF mutation.
2012: Erivedge (vismodegib): Treatment for advanced basal-cell carcinoma (BCC). A small molecule inhibitor that targets a key protein in the Hedgehog signaling pathway. This is the first approved therapy for advanced BCC.
2012: Perjeta (pertuzumab): For use in combination with Herceptin (trastuzumab) and docetaxel chemotherapy for the treatment of patients with previously untreated HER2-positive metastatic breast cancer.
2013: Kadcyla (ado-trastuzumab emtansine): The first Genentech antibody-drug conjugate (ADC) to receive FDA approval. It consists of trastuzumab (Herceptin) linked to a cytotoxic agent mertansine (DM1), used in the treatment of HER2-positive metastatic breast cancer.
2013: Gazyva (obinutuzumab): For use in combination with chlorambucil to treat patients with previously untreated chronic lymphocytic leukemia (CLL). Gazyva is the first drug with breakthrough therapy designation to receive FDA approval.
2014: Esbriet (pirfenidone): An anti-fibrotic drug for the treatment of idiopathic pulmonary fibrosis (IPF). Developed by Intermune, Inc.
2015: Cotellic (cobimetinib): For use in combination with ZELBORAF (vemurafenib), to treat metastatic melanoma caused by BRAF mutation.
2015: Alecensa (alectinib): Treatment for non-small cell lung cancer (NSCLC).
2016: Venclexta (venetoclax): Treatment for patients with chronic lymphocytic leukemia (CLL) who have a chromosomal abnormality called 17p deletion and who have been treated with at least one prior therapy.
2016: Tecentriq (atezolizumab): First-in-class anti-PD-L1 antibody for the treatment of advanced bladder cancer or metastatic non-small cell lung cancer (NSCLC), both after failure of platinum-based chemotherapy. Tecentriq was granted accelerated approval for its advanced bladder cancer indication due to promising phase II results.
2017: Ocrevus (ocrelizumab): The first FDA-approved therapy that treats both relapsing-remitting multiple sclerosis (RRMS) and primary progressive multiple sclerosis (PPMS). The PPMS form of the disease previously had no approved treatments.
2017: Hemlibra (emicizumab): Treatment for haemophilia A. Developed by Chugai Pharmaceutical Co.
2018: Xofluza (Baloxavir marboxil): Antiviral medication for treatment of influenza A and influenza B. Developed by Shionogi.
2019: Polivy (Polatuzumab vedotin-piiq): Treatment of diffuse large B-cell lymphoma when used in combination with bendamustine and rituximab.
See also
Evan Morris
References
Further reading
External links
Genentech Suppliers, Partners, and Customers
Corporate chronology (Genentech)
"A Cancer Drug Shows Promise, at a Price That Many Can't Pay", The New York Times, February 15, 2006, Alex Berenson
Presentation by Genentech employees about sustainable business January 10, 2007
1976 establishments in California
2009 mergers and acquisitions
American companies established in 1976
Biotechnology companies established in 1976
Biotechnology companies of the United States
Companies based in South San Francisco, California
Companies formerly listed on the New York Stock Exchange
Roche
Life sciences industry
Pharmaceutical companies established in 1976
Pharmaceutical companies of the United States
South San Francisco, California
University spin-offs
American subsidiaries of foreign companies | Genentech | [
"Biology"
] | 3,029 | [
"Life sciences industry"
] |
362,471 | https://en.wikipedia.org/wiki/Zygmunt%20Janiszewski | Zygmunt Janiszewski (12 July 1888 – 3 January 1920) was a Polish mathematician.
Early life and education
He was born to mother Julia Szulc-Chojnicka and father, Czeslaw Janiszewski who was a graduate of the University of Warsaw and served as the director of the Société du Crédit Municipal in Warsaw.
Janiszewski left Poland to study mathematics in Zürich, Munich and Göttingen, where he was taught by some of the most prominent mathematicians of the time, such as Heinrich Burkhardt, David Hilbert, Hermann Minkowski and Ernst Zermelo. He then went to Paris and in 1911 received his doctorate in topology under the supervision of Henri Lebesgue. His thesis was titled Sur les continus irréductibles entre deux points (On the Irreducible Continuous Curves Between Two Points). In 1913, he published a seminal work in the field of topology of surface entitled On Cutting the Plane by Continua.
Career
Janiszewski taught at the University of Lwów and was professor at the University of Warsaw. At the outbreak of World War I he was a soldier in the Polish Legions of Józef Piłsudski, and took part in operations around Volyn. Along with other officers, he refused to swear an oath of allegiance to the Austrian government. He subsequently left the Legions and went into hiding under an assumed identity, Zygmunt Wicherkiewicz, in Boiska, near Zwoleń. From Boiska he moved on to Ewin, near Włoszczowa, where he directed a shelter for homeless children.
In 1917 he published an article "O potrzebach matematyki w Polsce" ("On the Needs of Mathematics in Poland") in the journal Nauka Polska (Polish Learning), thus initiating the Polish School of Mathematics. He also founded the journal Fundamenta Mathematicae. Janiszewski proposed the journal's name in 1919, but the first issue was published only after his death in 1920.
Janiszewski devoted the family property that he had inherited from his father to charity and education. He also donated all the prize money that he received from mathematical awards and competitions to the education and development of young Polish students.
Death
Janiszewski was engaged to Janina Kelles-Krauz, daughter of Kazimierz Kelles-Krauz. The wedding date had been set, but he died before they could marry. His life was cut short by the influenza pandemic of 1918–19, at Lwów, on 3 January 1920, at age 31. He willed his body for medical research, and his cranium for craniological study, desiring to be "useful after his death".
Samuel Dickstein wrote a commemorative address after Janiszewski's death, honoring his humility, kindness and dedication to his work:
While Janiszewski is best remembered for his many contributions to topological mathematics in the early 20th century, for the founding of Fundamenta Mathematicae, and for his enthusiasm for teaching young minds, his loyalty to his homeland during World War I perhaps gives the greatest insight into his psyche. The orphans' shelter that he set up during the war doubtless saved many lives and was perhaps his greatest contribution to the world.
On 3 January 2020, the 100th anniversary of his death, a researcher from Australia traveled to Lviv and met with the director of Lychakiv Cemetery. Restoration of the grave was arranged, and the stone was restored. Janiszewski is buried in field 58, plot 82 of Lychakiv Cemetery.
See also
List of Poles – Mathematics
Notes
References
et passim.
External links
1888 births
1920 deaths
Warsaw School of Mathematics
People from Warsaw Governorate
Deaths from the Spanish flu pandemic
Topologists
University of Paris alumni | Zygmunt Janiszewski | [
"Mathematics"
] | 791 | [
"Topologists",
"Topology"
] |
362,477 | https://en.wikipedia.org/wiki/Antoni%20Zygmund | Antoni Zygmund (December 26, 1900 – May 30, 1992) was a Polish-American mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986.
Biography
Born in Warsaw, Zygmund obtained his Ph.D. from the University of Warsaw (1923) and was a professor at Stefan Batory University at Wilno from 1930 to 1939, when World War II broke out and Poland was occupied. In 1940 he managed to emigrate to the United States, where he became a professor at Mount Holyoke College in South Hadley, Massachusetts. In 1945–1947 he was a professor at the University of Pennsylvania, and from 1947, until his retirement, at the University of Chicago.
He was a member of several scientific societies. From 1930 until 1952 he was a member of the Warsaw Scientific Society (TNW), from 1946 of the Polish Academy of Learning (PAU), from 1959 of the Polish Academy of Sciences (PAN), and from 1961 of the National Academy of Sciences in the United States. In 1986 he received the National Medal of Science.
In 1935 Zygmund published in Polish the original edition of what has become, in its English translation, the two-volume Trigonometric Series. It was described by Robert A. Fefferman as "one of the most influential books in the history of mathematical analysis" and "an extraordinarily comprehensive and masterful presentation of a ... vast field". Jean-Pierre Kahane called the book "The Bible" of a harmonic analyst. The theory of trigonometric series had remained the largest component of Zygmund's mathematical investigations.
His work has had a pervasive influence in many fields of mathematics, mostly in mathematical analysis, and particularly in harmonic analysis. Among the most significant were the results he obtained with Calderón on singular integral operators. George G. Lorentz called it Zygmund's crowning achievement, one that "stands somewhat apart from the rest of Zygmund's work".
Zygmund's students included Alberto Calderón, Paul Cohen, Nathan Fine, Józef Marcinkiewicz, Victor L. Shapiro, Guido Weiss, Elias M. Stein and Mischa Cotlar. He died in Chicago.
Family
Antoni Zygmund, who had three sisters, married Irena Parnowska, a mathematician, in 1925. Upon his death he was survived by four grandsons.
Mathematical objects named after Zygmund
Calderón–Zygmund lemma
Marcinkiewicz–Zygmund inequality
Paley–Zygmund inequality
Calderón–Zygmund kernel
Books
Trigonometric Series (Cambridge University Press 1959, 2002)
Intégrales singulières (Springer-Verlag, 1971)
Trigonometric Interpolation (University of Chicago, 1950)
Measure and Integral: An Introduction to Real Analysis, With Richard L. Wheeden (Marcel Dekker, 1977)
Analytic Functions, with Stanislaw Saks (Elsevier Science Ltd, 1971)
See also
Calderón–Zygmund lemma
Zygmunt Janiszewski
Marcinkiewicz–Zygmund inequality
Paley–Zygmund inequality
List of Poles
Centipede mathematics
References
Further reading
Kazimierz Kuratowski, A Half Century of Polish Mathematics: Remembrances and Reflections, Oxford, Pergamon Press, 1980, .
External links
Mount Holyoke biography
1900 births
1992 deaths
People from Warsaw Governorate
20th-century Polish mathematicians
Mathematical analysts
National Medal of Science laureates
Members of the Polish Academy of Learning
University of Warsaw alumni
Mount Holyoke College faculty
University of Pennsylvania faculty
University of Chicago faculty
Academic staff of Vilnius University
Polish emigrants to the United States
Functional analysts
Members of the Polish Academy of Sciences
Members of the United States National Academy of Sciences | Antoni Zygmund | [
"Mathematics"
] | 826 | [
"Mathematical analysis",
"Mathematical analysts"
] |
362,481 | https://en.wikipedia.org/wiki/Karol%20Borsuk | Karol Borsuk (8 May 1905 – 24 January 1982) was a Polish mathematician. His main area of interest was topology. He made significant contributions to shape theory, a term which he coined. He also obtained important results in functional analysis. He was a professor of mathematics at the University of Warsaw, a member of the Polish Academy of Sciences, the Polish Mathematical Society and a leading representative of the Warsaw School of Mathematics.
Life and career
Early life and education
Borsuk was born in 1905 in Warsaw to father Marian, a surgeon, and mother Zofia (née Maciejewska). In 1923, he graduated from the Stanisław Staszic State Gymnasium in Warsaw. Between 1923–1927, he studied mathematics at the Faculty of Philosophy of the University of Warsaw.
He received his master's degree and doctorate from Warsaw University in 1927 and 1930, respectively. His PhD thesis title was On the Subject of Topological Characterization of Euclidean Spheres and his advisor was Stefan Mazurkiewicz. From 1929 to 1934, he worked at the Faculty of Mathematics at the University of Warsaw. He became a professor in 1938. In the interwar period, Borsuk visited Lwów, which was a thriving center of mathematics of the Second Polish Republic, and began his collaboration with Stanisław Ulam, especially in the field of topology. Borsuk joined the mathematicians in the Scottish Café and contributed to the open problems which they wrote down in the famous book.
World War II
During World War II, he run a stationary store and provided a secret meeting place for the Home Army. He designed and published a number of board games including Animal Husbandry, which enjoyed great popularity and was re-released in 1997 as Superfarmer. In the years 1939–1944, he gave secret lectures at the University of Warsaw. In 1943, he was arrested for his participation in the resistance movement and spent a couple of months at the Pawiak Prison. During the Warsaw Uprising in 1944, he was transported alongside his family to the Dulag 121 Camp in Pruszków. He managed to escape from the camp and remained in hiding until the end of the war.
Later career
In 1945, he completed a project in collaboration with Bronisław Knaster and Kazimierz Kuratowski concerning the establishment of the Institute of Mathematics of the Polish Academy of Sciences. In 1946, he returned to the University of Warsaw where he served as the Head of the Institute of Mathematics from 1952 to 1964. In 1952, he became a member of the Polish Academy of Sciences, and in 1953, a corresponding member of the Bulgarian Academy of Sciences. He was also a member of the Polish Mathematical Society. He worked as an editor-in-chief of Dissertationes Mathematicae and deputy editor-in-chief of Fundamenta Mathematicae. In 1946–47, he lectured at the Institute for Advanced Study at Princeton University, in 1959–60 at the University of California at Berkeley, in 1963–64 at the University of Wisconsin at Madison, and in 1967–68 at Rutgers University–New Brunswick. In 1954, he received the Officer's Cross of the Order of Polonia Restituta for his "outstanding contributions to science". In 1976, he was awarded an honorary doctorate by the University of Zagreb.
Borsuk's students include: Samuel Eilenberg, Andrzej Kirkor, Jan Jaworowski, Andrzej Granas, Antoni Kosiński, Karol Sieklucki, Włodzimierz Holsztyński, Rafał Molski, Hanna Patkowska, Andrzej Jankowski, Włodzimierz Kuperberg, Stanisław Spież, Krystyna Kuperberg, Jerzy Dydak, Andrzej Trybulec, Marian Orłowski, Alfred Surzycki.
Research
Borsuk introduced the theory of absolute retracts (ARs) and absolute neighborhood retracts (ANRs), and the cohomotopy groups, later called Borsuk–Spanier cohomotopy groups. He also founded shape theory. He has constructed various beautiful examples of topological spaces, e.g. an acyclic, 3-dimensional continuum which admits a fixed point free homeomorphism onto itself; also 2-dimensional, contractible polyhedra which have no free edge.
His topological and geometric conjectures and themes stimulated research for more than half a century; in particular, his open problems stimulated the infinite-dimensional topology. Some of the notable mathematical concepts that bear Borsuk's name include Borsuk's conjecture, Borsuk–Ulam theorem and Bing–Borsuk conjecture.
Private life
In 1936, he married Zofia Paczkowska. One of his two daughters, Magdalena, who was a Professor of Paleontology, was married to Polish mathematician Andrzej Białynicki-Birula. He died in Warsaw in 1982 and was buried at the Powązki Cemetery. In 2008, a commemorative plaque in honour of Borsuk was unveiled at the entrance to the tenement house in Warsaw at Filtrowa 63 Street where the mathematician used to live.
Works
Geometria analityczna w n wymiarach (1950) (translated to English as Multidimensional Analytic Geometry, Polish Scientific Publishers, 1969)
Podstawy geometrii (1955)
Foundations of Geometry (1960) with Wanda Szmielew, North Holland publisher
Theory of Retracts (1967), PWN, Warszawa.
Theory of Shape (1975)
Collected papers vol. I, (1983), PWN, Warszawa.
See also
Zygmunt Janiszewski
Stanislaw Ulam
Scottish Café
Ham sandwich theorem
References
External links
Warsaw School of Mathematics
Topologists
Members of the Polish Academy of Sciences
University of Warsaw alumni
Academic staff of the University of Warsaw
People from Warsaw Governorate
1905 births
1982 deaths
Prisoners of Dulag 121 Pruszków
Recipients of the Medal of the 10th Anniversary of the People's Republic of Poland | Karol Borsuk | [
"Mathematics"
] | 1,249 | [
"Topologists",
"Topology"
] |
362,499 | https://en.wikipedia.org/wiki/Ernest%20Walton | Ernest Thomas Sinton Walton (6 October 1903 – 25 June 1995) was an Irish nuclear physicist and Nobel laureate in Physics who first split the atom. He is best known for his work with John Cockcroft to construct one of the earliest types of particle accelerator, the Cockcroft–Walton generator. In experiments performed at Cambridge University in the early 1930s using the generator, Walton and Cockcroft became the first team to use a particle beam to transform one element to another. According to their Nobel Prize citation: "Thus, for the first time, a nuclear transmutation was produced by means entirely under human control".
Early years
Ernest Walton was born in Abbeyside, Dungarvan, County Waterford, to a Methodist minister father, the Rev. John Walton (1874–1936), who was from Cloughjordan in County Tipperary, and his wife, Anna Sinton (1874–1906), who was from Richhill in County Armagh. In those days a general clergyman's family moved once every three years, and this practice carried Ernest and his family, while he was a small child, to Rathkeale, County Limerick (where his mother died), and to County Monaghan. He attended day schools in counties Down and Tyrone, and at Wesley College Dublin before becoming a boarder at Methodist College Belfast in 1915, where he excelled in science and mathematics.
In 1922, Walton won scholarships to Trinity College Dublin for the study of mathematics and science, and would go on to be elected a Foundation Scholar in 1924. He was awarded bachelor's and master's degrees from Trinity in 1926 and 1927, respectively. During these years at college, Walton received numerous prizes for excellence in physics and mathematics (seven prizes in all), including the Foundation Scholarship in 1924. Following graduation, he was awarded an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851 and was accepted as a research student at Trinity College, Cambridge, under the supervision of Sir Ernest Rutherford, Director of Cambridge University's Cavendish Laboratory. At the time there were four Nobel Prize laureates on the staff at the Cavendish lab and a further five were to emerge, including Walton and John Cockcroft. Walton was awarded his PhD in 1931 and remained at Cambridge as a researcher until 1934.
During the early 1930s, Walton and John Cockcroft collaborated to build an apparatus that split the nuclei of lithium atoms by bombarding them with a stream of protons accelerated inside a high-voltage tube (700 kilovolts). The splitting of the lithium nuclei produced helium nuclei. They went on to use Boron and Carbon as targets for their 'disintegration' experiments, and to report artificially induced radioactivity. These experiments provided verification of theories about atomic structure that had been proposed earlier by Rutherford, George Gamow, and others. The successful apparatus – a type of particle accelerator now called the Cockcroft-Walton generator – helped to usher in an era of particle-accelerator-based experimental nuclear physics. It was this research at Cambridge in the early 1930s that won Walton and Cockcroft the Nobel Prize in Physics in 1951.
Career at Trinity College Dublin
Ernest Walton returned to Ireland in 1934 to become a fellow of Trinity College Dublin in the physics department, and in 1946 was appointed Erasmus Smith's Professor of Natural and Experimental Philosophy. Walton's lecturing was considered outstanding as he had the ability to present complicated matters in simple and easy-to-understand terms. His research interests were pursued with very limited resources, yet he was able to study, in the late 1950s, the phosphorescent effect in glasses, secondary-electron emissions from surfaces under positive-ion bombardment, radiocarbon dating and low-level counting, and the deposition of thin films on glass.
Walton was associated with the Dublin Institute for Advanced Studies for over 40 years, where he served long periods on the board of the School of Cosmic Physics and on the council of the Institute. Following the 1952 death of John J. Nolan, the inaugural chairman of the School of Cosmic Physics, Walton assumed the role and served in that position until 1960, when he was succeeded by John H. Poole.
Later years and death
Although he retired from Trinity College Dublin in 1974, he retained his association with the Physics Department at Trinity up to his final illness. Shortly before his death, he marked his lifelong devotion to Trinity by presenting his Nobel medal and citation to the College. Ernest Walton died in Belfast on 25 June 1995, aged 91. He is buried in Deansgrange Cemetery, Dublin.
Family life
Ernest Walton married Winifred Wilson, a Methodist minister's daughter, in 1934. Their four children are Alan Walton (a physicist at the University of Cambridge), Marian Woods, Philip Walton (Professor of Applied Physics, NUI Galway), and Jean Clarke. He served on a committee of Wesley College, Dublin.
Religious views
Raised as a Methodist, Walton has been described as someone who was strongly committed to the Christian faith. He gave lectures about the relationship of science and religion in several countries after he won the Nobel Prize, and he encouraged the progress of science as a way to know more about God.
Walton is quoted as saying:
Walton held an interest in topics about the government and the Church, and after his death, the organisation Christians in Science Ireland established the Walton Lectures on Science and Religion (an initiative similar to the Boyle Lectures). David Wilkinson, Denis Alexander, and others have given Walton Lectures in universities across Ireland.
Along with Lochlainn O'Raifeartaigh and Michael Fry, Walton helped found the Irish Pugwash group, opposing the nuclear weapons race.
Honours
Walton and John Cockcroft were recipients of the 1951 Nobel Prize in Physics for their "work on the transmutation of the atomic nuclei by artificially accelerated atomic particles" (popularly known as splitting the atom). They are credited with being the first to disintegrate the lithium nucleus by bombardment with accelerated protons (or hydrogen nuclei) and identifying helium nuclei in the products in 1930. More generally, they had built an apparatus which showed that nuclei of various lightweight elements (such as lithium) could be split by fast-moving protons.
In 1935, Walton was elected a member of the Royal Irish Academy (MRIA). Walton and Cockcroft received the Hughes Medal of the Royal Society of London in 1938. In much later years – predominantly after his retirement in 1974 – Walton received honorary degrees or conferrals from numerous Irish, British, and North American institutions.
The "Walton Causeway Park" in Walton's native Dungarvan was dedicated in his honour with Walton himself attending the ceremony in 1989. After his death the Waterford Institute of Technology named a building the ETS Walton Building and a plaque was placed on the site of his birthplace.
Other honours for Walton include the Walton Building at Methodist College Belfast, the school where he had been a boarder for five years, and a memorial plaque outside the main entrance to Methodist College. Wesley College in Dublin, where he attended and for many years served as chairman of the board of Governors, established the Walton Prize for Physics, and a prize with the same name at Methodist College is awarded to the pupil who obtains the highest marks in A Level Physics. There is also a scholarship in Waterford named after Walton. In 2014, Trinity College Dublin set up the Trinity Walton Club, an extracurricular STEM Education centre for teenagers.
References
Further reading
External links
Ernest Thomas Sinton Walton: Memorial Discourse by Dr. Vincent McBrierty, 16 April 2012
Annotated bibliography for Ernest Walton from the Alsos Digital Library for Nuclear Issues
Ernest Thos S Walton 1911 Census of Ireland.
BBC Archive – an interview with Professor Ernest Walton Recorded 1985, duration 43min.
The Papers of E T S Walton held at Churchill Archives Centre
1903 births
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Academics of Trinity College Dublin
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People educated at Cookstown High School
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Scientists from County Waterford
Scholars and academics from County Waterford | Ernest Walton | [
"Physics"
] | 1,672 | [
"Experimental physics",
"Experimental physicists"
] |
362,501 | https://en.wikipedia.org/wiki/Samuel%20Eilenberg | Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra.
Early life and education
He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia University.
He earned his Ph.D. from University of Warsaw in 1936, with thesis On the Topological Applications of Maps onto a Circle; his thesis advisors were Kazimierz Kuratowski and Karol Borsuk. He died in New York City in January 1998.
Career
Eilenberg's main body of work was in algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (and the Eilenberg–Steenrod axioms are named for the pair), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.
Eilenberg was a member of Bourbaki and, with Henri Cartan, wrote the 1956 book Homological Algebra.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules.
Eilenberg contributed to automata theory and algebraic automata theory. In particular, he introduced a model of computation called X-machine and a new prime decomposition algorithm for finite state machines in the vein of Krohn–Rhodes theory.
Art collection
Eilenberg was also a prominent collector of Asian art. His collection mainly consisted of small sculptures and other artifacts from India, Indonesia, Nepal, Thailand, Cambodia, Sri Lanka and Central Asia. In 1991–1992, the Metropolitan Museum of Art in New York staged an exhibition from more than 400 items that Eilenberg had donated to the museum, entitled The Lotus Transcendent: Indian and Southeast Asian Art From the Samuel Eilenberg Collection. In reciprocity, the Metropolitan Museum of Art donated substantially to the endowment of the Samuel Eilenberg Visiting Professorship in Mathematics at Columbia University.
Selected publications
See also
Stefan Banach
Stanislaw Ulam
Eilenberg–Montgomery fixed point theorem
Footnotes
External links
Eilenberg's biography − from the National Academies Press, by Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller and Saunders Mac Lane.
1913 births
1998 deaths
20th-century American mathematicians
Category theorists
Columbia University faculty
Nicolas Bourbaki
Scientists from New York City
Warsaw School of Mathematics
People from Warsaw Governorate
Polish emigrants to the United States
20th-century Polish Jews
Topologists
University of Warsaw alumni
Wolf Prize in Mathematics laureates
Members of the United States National Academy of Sciences
Mathematicians from New York (state) | Samuel Eilenberg | [
"Mathematics"
] | 570 | [
"Mathematical structures",
"Topologists",
"Topology",
"Category theory",
"Category theorists"
] |
362,536 | https://en.wikipedia.org/wiki/Henri%20Cartan | Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology.
He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer , physicist and mathematician , and the son-in-law of physicist Pierre Weiss.
Life
According to his own words, Henri Cartan was interested in mathematics at a very young age, without being influenced by his family. He moved to Paris with his family after his father's appointment at Sorbonne in 1909 and he attended secondary school at Lycée Hoche in Versailles.
In 1923 he started studying mathematics at École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928. His PhD thesis, entitled Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, was supervised by Paul Montel.
Cartan taught at Lycée Malherbe in Caen from 1928 to 1929, at the University of Lille from 1929 to 1931 and at the University of Strasbourg from 1931 to 1939. After the German invasion of France the university staff was moved to Clermont Ferrand, but in 1940 he returned to Paris to work at Université de Paris and École Normale Supérieure. From 1969 until his retirement in 1975 he was professor at Paris-Sud University.
Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in Die, Drome.
Honours and awards
In 1932 Cartan was invited to give a Cours Peccot at the Collège de France. In 1950 he was elected president of the Société mathématique de France and from 1967 to 1970 he was president of the International Mathematics Union. He was awarded the Émile Picard Medal in 1959, the CNRS Gold Medal in 1976, and the Wolf Prize in 1980.
He was an invited Speaker at the International Congress of Mathematics in 1932 in Zürich and a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts and in 1958 in Edinburgh.
From 1974 until his death he had been a member of the French Academy of Sciences. He was elected a foreign member of many academies and societies, including the American Academy of Arts and Sciences (1950), London Mathematical Society (1959), Royal Danish Academy of Sciences and Letters (1962), (1967), Royal Society of London (1971), Göttingen Academy of Sciences and Humanities (1971), Spanish Royal Academy of Sciences (1971), United States National Academy of Sciences (1972), Bavarian Academy of Science (1974), Royal Academy of Belgium (1978), Japan Academy (1979), Finnish Academy of Science and Letters (1979), Royal Swedish Academy of Sciences (1981), Polish Academy of Sciences (1985) and Russian Academy of Sciences (1999).
He was awarded Honorary Doctorates from Münster (1952), ETH Zürich (1955), Oslo (1961), Sussex (1969), Cambridge (1969), Stockholm (1978), Oxford University (1980), Zaragoza (1985) and Athens (1992).
The French government named him Commandeur des Palmes Académiques in 1964, Officier de la Légion d'honneur in 1965 and Commandeur de l'Ordre du Mérite in 1971.
Political and social activities
During the 70's and the 80's Cartan used his influence to help obtain the release of several dissident mathematicians, including Leonid Plyushch and Anatoly Shcharansky, imprisoned by the Soviet Union, Jose Luis Massera, imprisoned between 1975 and 1984 by the Uruguayan dictatorship, and Sion Assidon, imprisoned during the Moroccan Years of Lead. For his humanitarian efforts, he received in 1989 the Heinz R. Pagels Human Rights of Scientists Award from the New York Academy of Sciences.
Since the 30's Cartan had tight collaborations with many German mathematicians, including Heinrich Behnke and Peter Thullen. Right after World War II he put many efforts to improve the cooperation between French and German mathematicians and restore the flow of exchanges of ideas and students.
Cartan supported the idea of European Federalism and from 1974 to 1985 was president of the French section of the Union of European Federalists. At the 1984 European elections he was the leader of the Liste pour les États-Unis d'Europe, which obtained 0.4% of votes and did not elect any candidate.
In 1992 he gave a speech at the first European Congress of Mathematics in Paris, remarking the common heritage and future of European countries and praising the first reunion between mathematicians from the two previously separated parts of Europe.
Research
Cartan worked in several fields across algebra, geometry and analysis, focussing primarily on algebraic topology and homological algebra.
He was a founding member of the Bourbaki group in 1934 and one of its most active participants. After 1945 he started his own seminar in Paris, which deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Joséphine Guidy Wandja (the first African woman to gain a PhD in mathematics), Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Cartan's first research interests, until the 40's, were in the theory of functions of several complex variables, which later gave rise to the theory of complex varieties and analytic geometry. Motivated by the solution to the Cousin problems, he worked on sheaf cohomology and coherent sheaves and proved two powerful results, Cartan's theorems A and B.
Since the 50's he became more interested in algebraic topology. Among his major contributions, he worked on cohomology operations and homology of the Eilenberg–MacLane spaces, he introduced the notion of Steenrod algebra, and, together with Jean-Pierre Serre, developed the method of "killing homotopy groups". His 1956 book with Samuel Eilenberg on homological algebra was an important text, treating the subject with a moderate level of abstraction with the help of category theory. They introduced fundamental concepts, including those of projective module, weak dimension, and what is now called the Cartan–Eilenberg resolution.
Among his other contributions, in general topology he introduced the notions of filter and ultrafilter and in potential theory he developed the fine topology and proved Cartan's lemma. The Cartan model for equivariant cohomology is also named after him.
Selected publications
Espaces fibrés et homotopie, (Séminaire Henri Cartan Tome 2 (1949–1950))
Cohomologie des groupes, suite spectrale, faisceaux, (Séminaire Henri Cartan Tome 3 (1950–1951))
Algèbres d'Eilenberg – Mac Lane et homotopie, (Séminaire Henri Cartan Tome 7 no2. (1954–1955))
Fonctions automorphes,(Séminaire Henri Cartan Tome 10 no2. (1957–1958))
Quelques questions de topologie, 1958.
Homological Algebra (with S. Eilenberg), Princeton Univ Press, 1956
Séminaires de l'École normale supérieure (called "Séminaires Cartan"), Secr. Math. IHP, 1948–1964; New York, W.A.Benjamin ed., 1967.
Théorie élémentaire des fonctions analytiques, Paris, Hermann, 1961 (translated into English, German, Japanese, Spanish and Russian).
Calcul différentiel, Paris, Hermann, 1967 (translated into English, Spanish and Russian).
Formes différentielles, Paris, Hermann, 1967 (translated into English, Spanish and Russian).
Differential Forms, Dover 2006
Œuvres — Collected Works, 3 vols., ed. Reinhold Remmert & Jean-Pierre Serre, Springer Verlag, Heidelberg, 1967.
Relations d'ordre en théorie des permutations des ensembles finis, Neuchâtel, 1973.
Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Paris, Hermann, 1975.
Cours de calcul différentiel, Paris, Hermann, 1977.
.
Notes
External links
Illusie, Luc; Cartier, Pierre (ed.), Dossier. Notices of the American Mathematical Society, Sept. 2010, ,
Biographical sketch and bibliography by the Société Mathématique de France on the occasion of Cartan's 100th birthday.
(translations of above two articles from the SMF Gazette)
Papers by Henri Cartan as member of the 'Association européenne des enseignants' (AEDE) and the 'Mouvement fédéraliste européen' (MFE) are at the Historical Archives of the EU in Florence
1904 births
2008 deaths
French men centenarians
20th-century French mathematicians
21st-century French mathematicians
Nicolas Bourbaki
Topologists
Complex analysts
French mathematical analysts
Academic staff of the Lille University of Science and Technology
Academic staff of the University of Strasbourg
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Presidents of the International Mathematical Union | Henri Cartan | [
"Mathematics"
] | 2,011 | [
"Topologists",
"Topology"
] |
362,565 | https://en.wikipedia.org/wiki/Optimal%20control | Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.
Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of variations by Edward J. McShane. Optimal control can be seen as a control strategy in control theory.
General method
Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. A control problem includes a cost functional that is a function of state and control variables. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost function. The optimal control can be derived using Pontryagin's maximum principle (a necessary condition also known as Pontryagin's minimum principle or simply Pontryagin's principle), or by solving the Hamilton–Jacobi–Bellman equation (a sufficient condition).
We begin with a simple example. Consider a car traveling in a straight line on a hilly road. The question is, how should the driver press the accelerator pedal in order to minimize the total traveling time? In this example, the term control law refers specifically to the way in which the driver presses the accelerator and shifts the gears. The system consists of both the car and the road, and the optimality criterion is the minimization of the total traveling time. Control problems usually include ancillary constraints. For example, the amount of available fuel might be limited, the accelerator pedal cannot be pushed through the floor of the car, speed limits, etc.
A proper cost function will be a mathematical expression giving the traveling time as a function of the speed, geometrical considerations, and initial conditions of the system. Constraints are often interchangeable with the cost function.
Another related optimal control problem may be to find the way to drive the car so as to minimize its fuel consumption, given that it must complete a given course in a time not exceeding some amount. Yet another related control problem may be to minimize the total monetary cost of completing the trip, given assumed monetary prices for time and fuel.
A more abstract framework goes as follows. Minimize the continuous-time cost functional
subject to the first-order dynamic constraints (the state equation)
the algebraic path constraints
and the endpoint conditions
where is the state, is the control, is the independent variable (generally speaking, time), is the initial time, and is the terminal time. The terms and are called the endpoint cost and the running cost respectively. In the calculus of variations, and are referred to as the Mayer term and the Lagrangian, respectively. Furthermore, it is noted that the path constraints are in general inequality constraints and thus may not be active (i.e., equal to zero) at the optimal solution. It is also noted that the optimal control problem as stated above may have multiple solutions (i.e., the solution may not be unique). Thus, it is most often the case that any solution to the optimal control problem is locally minimizing.
Linear quadratic control
A special case of the general nonlinear optimal control problem given in the previous section is the linear quadratic (LQ) optimal control problem. The LQ problem is stated as follows. Minimize the quadratic continuous-time cost functional
Subject to the linear first-order dynamic constraints
and the initial condition
A particular form of the LQ problem that arises in many control system problems is that of the linear quadratic regulator (LQR) where all of the matrices (i.e., , , , and ) are constant, the initial time is arbitrarily set to zero, and the terminal time is taken in the limit (this last assumption is what is known as infinite horizon). The LQR problem is stated as follows. Minimize the infinite horizon quadratic continuous-time cost functional
Subject to the linear time-invariant first-order dynamic constraints
and the initial condition
In the finite-horizon case the matrices are restricted in that and are positive semi-definite and positive definite, respectively. In the infinite-horizon case, however, the matrices and are not only positive-semidefinite and positive-definite, respectively, but are also constant. These additional restrictions on
and in the infinite-horizon case are enforced to ensure that the cost functional remains positive. Furthermore, in order to ensure that the cost function is bounded, the additional restriction is imposed that the pair is controllable. Note that the LQ or LQR cost functional can be thought of physically as attempting to minimize the control energy (measured as a quadratic form).
The infinite horizon problem (i.e., LQR) may seem overly restrictive and essentially useless because it assumes that the operator is driving the system to zero-state and hence driving the output of the system to zero. This is indeed correct. However the problem of driving the output to a desired nonzero level can be solved after the zero output one is. In fact, it can be proved that this secondary LQR problem can be solved in a very straightforward manner. It has been shown in classical optimal control theory that the LQ (or LQR) optimal control has the feedback form
where is a properly dimensioned matrix, given as
and is the solution of the differential Riccati equation. The differential Riccati equation is given as
For the finite horizon LQ problem, the Riccati equation is integrated backward in time using the terminal boundary condition
For the infinite horizon LQR problem, the differential Riccati equation is replaced with the algebraic Riccati equation (ARE) given as
Understanding that the ARE arises from infinite horizon problem, the matrices , , , and are all constant. It is noted that there are in general multiple solutions to the algebraic Riccati equation and the positive definite (or positive semi-definite) solution is the one that is used to compute the feedback gain. The LQ (LQR) problem was elegantly solved by Rudolf E. Kálmán.
Numerical methods for optimal control
Optimal control problems are generally nonlinear and therefore, generally do not have analytic solutions (e.g., like the linear-quadratic optimal control problem). As a result, it is necessary to employ numerical methods to solve optimal control problems. In the early years of optimal control ( 1950s to 1980s) the favored approach for solving optimal control problems was that of indirect methods. In an indirect method, the calculus of variations is employed to obtain the first-order optimality conditions. These conditions result in a two-point (or, in the case of a complex problem, a multi-point) boundary-value problem. This boundary-value problem actually has a special structure because it arises from taking the derivative of a Hamiltonian. Thus, the resulting dynamical system is a Hamiltonian system of the form
where
is the augmented Hamiltonian and in an indirect method, the boundary-value problem is solved (using the appropriate boundary or transversality conditions). The beauty of using an indirect method is that the state and adjoint (i.e., ) are solved for and the resulting solution is readily verified to be an extremal trajectory. The disadvantage of indirect methods is that the boundary-value problem is often extremely difficult to solve (particularly for problems that span large time intervals or problems with interior point constraints). A well-known software program that implements indirect methods is BNDSCO.
The approach that has risen to prominence in numerical optimal control since the 1980s is that of so-called direct methods. In a direct method, the state or the control, or both, are approximated using an appropriate function approximation (e.g., polynomial approximation or piecewise constant parameterization). Simultaneously, the cost functional is approximated as a cost function. Then, the coefficients of the function approximations are treated as optimization variables and the problem is "transcribed" to a nonlinear optimization problem of the form:
Minimize
subject to the algebraic constraints
Depending upon the type of direct method employed, the size of the nonlinear optimization problem can be quite small (e.g., as in a direct shooting or quasilinearization method), moderate (e.g. pseudospectral optimal control) or may be quite large (e.g., a direct collocation method). In the latter case (i.e., a collocation method), the nonlinear optimization problem may be literally thousands to tens of thousands of variables and constraints. Given the size of many NLPs arising from a direct method, it may appear somewhat counter-intuitive that solving the nonlinear optimization problem is easier than solving the boundary-value problem. It is, however, the fact that the NLP is easier to solve than the boundary-value problem. The reason for the relative ease of computation, particularly of a direct collocation method, is that the NLP is sparse and many well-known software programs exist (e.g., SNOPT) to solve large sparse NLPs. As a result, the range of problems that can be solved via direct methods (particularly direct collocation methods which are very popular these days) is significantly larger than the range of problems that can be solved via indirect methods. In fact, direct methods have become so popular these days that many people have written elaborate software programs that employ these methods. In particular, many such programs include DIRCOL, SOCS, OTIS, GESOP/ASTOS, DITAN. and PyGMO/PyKEP. In recent years, due to the advent of the MATLAB programming language, optimal control software in MATLAB has become more common. Examples of academically developed MATLAB software tools implementing direct methods include RIOTS, DIDO, DIRECT, FALCON.m, and GPOPS, while an example of an industry developed MATLAB tool is PROPT.<ref>Rutquist, P. and Edvall, M. M, PROPT – MATLAB Optimal Control Software," 1260 S.E. Bishop Blvd Ste E, Pullman, WA 99163, USA: Tomlab Optimization, Inc.</ref> These software tools have increased significantly the opportunity for people to explore complex optimal control problems both for academic research and industrial problems. Finally, it is noted that general-purpose MATLAB optimization environments such as TOMLAB have made coding complex optimal control problems significantly easier than was previously possible in languages such as C and FORTRAN.
Discrete-time optimal control
The examples thus far have shown continuous time systems and control solutions. In fact, as optimal control solutions are now often implemented digitally, contemporary control theory is now primarily concerned with discrete time systems and solutions. The Theory of Consistent Approximations provides conditions under which solutions to a series of increasingly accurate discretized optimal control problem converge to the solution of the original, continuous-time problem. Not all discretization methods have this property, even seemingly obvious ones. For instance, using a variable step-size routine to integrate the problem's dynamic equations may generate a gradient which does not converge to zero (or point in the right direction) as the solution is approached. The direct method RIOTS'' is based on the Theory of Consistent Approximation.
Examples
A common solution strategy in many optimal control problems is to solve for the costate (sometimes called the shadow price) . The costate summarizes in one number the marginal value of expanding or contracting the state variable next turn. The marginal value is not only the gains accruing to it next turn but associated with the duration of the program. It is nice when can be solved analytically, but usually, the most one can do is describe it sufficiently well that the intuition can grasp the character of the solution and an equation solver can solve numerically for the values.
Having obtained , the turn-t optimal value for the control can usually be solved as a differential equation conditional on knowledge of . Again it is infrequent, especially in continuous-time problems, that one obtains the value of the control or the state explicitly. Usually, the strategy is to solve for thresholds and regions that characterize the optimal control and use a numerical solver to isolate the actual choice values in time.
Finite time
Consider the problem of a mine owner who must decide at what rate to extract ore from their mine. They own rights to the ore from date to date . At date there is ore in the ground, and the time-dependent amount of ore left in the ground declines at the rate of that the mine owner extracts it. The mine owner extracts ore at cost (the cost of extraction increasing with the square of the extraction speed and the inverse of the amount of ore left) and sells ore at a constant price . Any ore left in the ground at time cannot be sold and has no value (there is no "scrap value"). The owner chooses the rate of extraction varying with time to maximize profits over the period of ownership with no time discounting.
See also
Active inference
Bellman equation
Bellman pseudospectral method
Brachistochrone
DIDO
DNSS point
Dynamic programming
Gauss pseudospectral method
Generalized filtering
GPOPS-II
CasADi
JModelica.org (Modelica-based open source platform for dynamic optimization)
Kalman filter
Linear-quadratic regulator
Model Predictive Control
Overtaking criterion
PID controller
PROPT (Optimal Control Software for MATLAB)
Pseudospectral optimal control
Pursuit-evasion games
Sliding mode control
SNOPT
Stochastic control
Trajectory optimization
References
Further reading
External links
Computational Optimal Control
Dr. Benoît CHACHUAT: Automatic Control Laboratory – Nonlinear Programming, Calculus of Variations and Optimal Control.
DIDO - MATLAB tool for optimal control
GEKKO - Python package for optimal control
GESOP – Graphical Environment for Simulation and OPtimization
GPOPS-II – General-Purpose MATLAB Optimal Control Software
CasADi – Free and open source symbolic framework for optimal control
PROPT – MATLAB Optimal Control Software
OpenOCL – Open Optimal Control Library
Elmer G. Wiens: Optimal Control – Applications of Optimal Control Theory Using the Pontryagin Maximum Principle with interactive models.
On Optimal Control by Yu-Chi Ho
Pseudospectral optimal control: Part 1
Pseudospectral optimal control: Part 2
Lecture Recordings and Script by Prof. Moritz Diehl, University of Freiburg on Numerical Optimal Control
Mathematical optimization | Optimal control | [
"Mathematics"
] | 3,060 | [
"Mathematical optimization",
"Mathematical analysis"
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362,594 | https://en.wikipedia.org/wiki/Hercules%20%28constellation%29 | Hercules is a star named after Hercules, the superhero adapted from the Greek hero Heracles. Hercules was one of the 48 constellations listed by the second-century astronomer Ptolemy, and it remains one of the 88 modern constellations today. It is the fifth-largest of the modern constellations and is the largest of the 50 which have no stars brighter than apparent magnitude +2.5.
Characteristics
Hercules is bordered by Draco to the north; Boötes, Corona Borealis, and Serpens Caput to the west; Ophiuchus to the south; Aquila to the southwest; and Sagitta, Vulpecula, and Lyra to the east. Covering 1225.1 square degrees and 2.970% of the night sky, it ranks fifth among the 88 constellations in size. The three-letter abbreviation for the constellation, as adopted by the International Astronomical Union in 1922, is 'Her'. The official constellation boundaries, as set by Eugène Delporte in 1930, are defined by a polygon of 32 segments (illustrated in infobox). In the equatorial coordinate system, epoch 2000, the right ascension coordinates of these borders lie between and , while the declination coordinates are between +3.67° and +51.32°. In mid-northern latitudes, Hercules is best observed from mid-spring until early autumn, culminating at midnight on June 13.
The solar apex is the direction of the open motion with respect to the Local Standard of Rest. This is located within the constellation of Hercules, around coordinates right ascension and declination . The north pole of the supergalactic coordinate system is located within this constellation at right ascension and declination .
Stars
Hercules has no first or second magnitude stars. However, it does have several stars above magnitude 4. Alpha Herculis, traditionally called Rasalgethi, is a triple star system, partly resolvable in small amateur telescopes, 359 light-years from Earth. Its common name means "the kneeler's head". The primary is an irregular variable star; it is a bright giant with a minimum magnitude of 4 and a maximum magnitude of 3. It has a diameter of roughly 400 solar diameters. The secondary, a spectroscopic binary that orbits the primary every 3600 years, is a blue-green hued star of magnitude 5.6. Beta Herculis, also called Kornephoros, is the brightest star in Hercules. It is a yellow giant of magnitude 2.8, 148 light-years from Earth; kornephoros means club-bearer. Delta Herculis A is a double star divisible in small amateur telescopes. The primary is a blue-white star of magnitude 3.1, and is 78 light-years from Earth. The optical companion is of magnitude 8.2. Gamma Herculis is also a double star divisible in small amateur telescopes. The primary is a white giant of magnitude 3.8, 195 light-years from Earth. The optical companion, widely separated, is 10th magnitude. Zeta Herculis is a binary star that is becoming divisible in medium-aperture amateur telescopes, as the components widen to their peak in 2025. The system, 35 light-years from Earth, has a period of 34.5 years. The primary is a yellow-tinged star of magnitude 2.9 and the secondary is an orange star of magnitude 5.7.
Hercules hosts further quite bright double stars and binary stars. Kappa Herculis is a double star divisible in small amateur telescopes. The primary is a yellow giant of magnitude 5.0, 388 light-years from Earth; the secondary is an orange giant of magnitude 6.3, 470 light-years from Earth. Rho Herculis is a binary star 402 light-years from Earth, divisible in small amateur telescopes. Both components are blue-green giant stars; the primary is magnitude 4.5 and the secondary is magnitude 5.5. 95 Herculis is a binary star divisible in small telescopes, 470 light-years from Earth. The primary is a silvery giant of magnitude 4.9, and the secondary is an old, reddish giant star of magnitude 5.2. The star HD164669 near the primary may be an optical double. 100 Herculis is a double star easily divisible in small amateur telescopes. Both components are magnitude 5.8 blue-white stars; they are 165 and 230 light-years from Earth.
There are several dimmer variable stars in Hercules. 30 Herculis, also called g Herculis, is a semiregular red giant with a period of 3 months. 361 light-years from Earth, it has a minimum magnitude of 6.3 and a maximum magnitude of 4.3. 68 Herculis, also called u Herculis, is a Beta Lyrae-type eclipsing binary star. 865 light-years from Earth, it has a period of 2 days; its minimum magnitude is 5.4 and its maximum magnitude is 4.7.
Mu Herculis is 27.4 light-years from Earth. The solar apex, i.e., the point on the sky which marks the direction that the Sun is moving in its orbit around the center of the Milky Way, narrowly figures in Hercules, between Hercules' left elbow (near Omicron Herculis) and Vega (in neighboring Lyra).
Planetary systems
Fifteen stars in Hercules are known to be orbited by extrasolar planets.
14 Herculis has two planets. The planet 14 Herculis b had the longest period (4.9 years) and widest orbit (2.8 AU) at the time of discovery. The planet 14 Herculis c orbits much further out with very low eccentricity. It was discovered in 2005 but was only confirmed in 2021.
HD 149026 has a transiting hot Jupiter planet.
HD 154345 has the planet HD 154345 b, a long period (9.095 years) and wide orbit (4.18 AU).
HD 164922 has the first long period Saturn-like planet discovered. The mass is 0.36 MJ and semimajor axis of 2.11 AU. More planets have been discovered since.
HD 147506 has the most massive transiting planet HAT-P-2b at the time of discovery. The mass is 8.65 MJ.
HD 155358 has two planets around the lowest metallicity planet-harboring star (21% Sun). Both planets orbit in mild eccentricities.
GSC 03089-00929 has a short transiting planet TrES-3b. The period was 31 hours.
Gliese 649 has a saturnian planet around the red dwarf star.
HD 156668 has an Earth mass planet with a minimum mass of four Earth masses.
HD 164595 is a G-type star with one known planet, HD 164595 b.
TOI-561 has four, or possibly five planets. The innermost of which, TOI-561 b, is notable because it is an ultra-short period planet.
Deep-sky objects
Hercules contains two bright globular clusters: M13, the brightest globular cluster in the northern hemisphere, and M92. It also contains the nearly spherical planetary nebula Abell 39. M13 lies between the stars η Her and ζ Her; it is dim, but may be detected by the unaided eye on a very clear night.
M13, visible to both the naked eye and binoculars, is a globular cluster of the 6th magnitude that contains more than 300,000 stars and is 25,200 light-years from Earth. It is also very large, with an apparent diameter of over 0.25 degrees, half the size of the full moon; its physical diameter is more than 100 light-years. Individual stars in M13 are resolvable in a small amateur telescope.
M92 is a globular cluster of magnitude 6.4, 26,000 light-years from earth. It is a Shapley class IV cluster, indicating that it is quite concentrated at the center; it has a very clear nucleus. M92 is visible as a fuzzy star in binoculars, like M13; it is denser and smaller than the more celebrated cluster. The oldest globular cluster known at 14 billion years, its stars are resolvable in a medium-aperture amateur telescope.
NGC 6229 is a dimmer globular cluster, with a magnitude of 9.4, it is the third-brightest globular in the constellation. 100,000 light-years from Earth, it is a Shapley class IV cluster, meaning that it is fairly rich in the center and quite concentrated at the nucleus.
NGC 6210 is a planetary nebula of the 9th magnitude, 4000 light-years from Earth visible as a blue-green elliptical disk in amateur telescopes larger than 75 mm in aperture.
AT2018cow, a large astronomical explosion detected on 16 June 2018. As of 22 June 2018, this astronomical event has generated a very large amount of interest among astronomers throughout the world and may be, as of 22 June 2018, considered a supernova tentatively named Supernova 2018cow.
The Hercules Cluster (Abell 2151) is a cluster of galaxies in Hercules.
The brightest radio source in the constellation is Hercules A, an elliptical galaxy located 2.1 billion light years away with a supermassive black hole with a mass of 2.5-billion-solar-mass that has radio jets that extend for one-and-a-half million light-years. Another bright radio source in Hercules is the quasar 3C 345 which has a jet that appears to move faster than the speed of light.
The Hercules–Corona Borealis Great Wall, the largest structure in the universe, is in Hercules.
Visualizations
Traditional
The traditional visualization imagines α Herculis as Hercules's head; its name, Rasalgethi, literally means "head of the kneeling one". Hercules's left hand then points toward Lyra from his shoulder (δ Herculis), and β Herculis, or Kornephoros ("club-bearer") forms his other shoulder. His narrow waist is formed by ε Herculis and ζ Herculis. His right leg is kneeling. Finally, his left leg (with θ Herculis as the knee and ι Herculis the foot) is stepping on Draco's head, the dragon/snake whom Hercules has vanquished and perpetually gloats over for eternities.
Keystone asterism
A common form found in modern star charts uses the quadrangle formed by π Her, η Her, ζ Her and ε Her (known as the "Keystone" asterism) as the lower half (abdomen) of Hercules's torso.
H.A. Rey
H. A. Rey has suggested an alternative visualization in which the "Keystone" becomes Hercules's head. This quadrangle lies between two very bright stars: Vega in the constellation Lyra and α CrB (Alphecca) in the constellation Corona Borealis. The hero's right leg contains two bright stars of the third magnitude: α Her (Rasalgethi) and δ Her (Sarin). The latter is the right knee. The hero's left leg contains dimmer stars of the fourth magnitude which do not have Bayer designations but which do have Flamsteed numbers. The star β Her belongs to the hero's outstretched right hand, and is also called Kornephoros.
History
According to Gavin White, the Greek constellation of Hercules is a distorted version of the Babylonian constellation known as the "Standing Gods" (MUL.DINGIR.GUB.BA.MESH). White argues that this figure was, like the similarly named "Sitting Gods", depicted as a man with a serpent's body instead of legs (the serpent element now being represented on the Greek star map by the figure of Draco that Hercules crushes beneath his feet). He further argues that the original name of Hercules – the 'Kneeler' (see below) – is a conflation of the two Babylonian constellations of the Sitting and Standing Gods.
The constellation is also sometimes associated with Gilgamesh, a Sumerian mythological hero. Phoenician tradition is said to have associated this constellation with their sun god, who slew a dragon (Draco).
The earliest Greek references to the constellation do not refer to it as Hercules. Aratus describes it as follows:
Right there in its [Draco's] orbit wheels a Phantom form, like to a man that strives at a task. That sign no man knows how to read clearly, nor what task he is bent, but men simply call him On His Knees. [ "the Kneeler"].
Now that Phantom, that toils on his knees, seems to sit on bended knee, and from both his shoulders his hands are upraised and stretch, one this way, one that, a fathom's length. Over the middle of the head of the crooked Dragon, he has the tip of his right foot. Here too that Crown [Corona], which glorious Dionysus set to be memorial of the dead Ariadne, wheels beneath the back of the toil-spent Phantom. To the Phantom's back the Crown is near, but by his head mark near at hand the head of Ophiuchus [...] Yonder, too, is the tiny Tortoise, which, while still beside his cradle, Hermes pierced for strings and bade it be called the Lyre [Lyra]: and he brought it into heaven and set it in front of the unknown Phantom. That Croucher on his Knees comes near the Lyre with his left knee, but the top of the Bird's head wheels on the other side, and between the Bird's head and the Phantom's knee is enstarred the Lyre.
The constellation is connected with Hercules in (probably 1st century BCE/CE, and attributed to Hyginus), which describes several different myths about the constellation:
Eratosthenes (3rd century BCE) is said to have described it as Hercules, placed above Draco (representing the dragon of the Hesperides) and preparing to fight it, holding his lion's skin in his left hand, and a club in his right (this can be found in the ).
Panyassis' (5th century BCE) reportedly said Jupiter was impressed by this fight, and made it a constellation, with Hercules kneeling on his right knee, and trying to crush Draco's head with his left foot, while striking with his right hand and holding the lion skin in his left.
Araethus (3rd/4th century BCE) is said to have described the constellation as depicting Ceteus son of Lycaon, imploring the gods to restore his daughter Megisto who had been transformed into a bear.
Hegesianax (2nd/3rd century BCE), who it says describes it as Theseus lifting the stone at Troezen.
Anacreon of Alexandria, who it claims also supports the idea that it depicts Theseus, saying that the constellation Lyra (said to be Theseus' lyre in other sources) is near Theseus.
Thamyris blinded by the Muses, kneeling in supplication.
Orpheus killed by the women of Thracia for seeing the sacred rituals of Liber (Dionysus).
Aeschylus' lost play Prometheus Unbound (5th century BCE), which recounted that when Hercules drives the cattle of Geryon through Liguria (northern Italy), the Ligurians will join forces and attack him, attempting to steal the cattle. Hercules fights until his weapons break, before falling to his knees, wounded. Jupiter, taking pity on his son, provides many stones on the ground, which Hercules uses to fight off the Ligurians. In commemoration of this, Jupiter makes a constellation depicting Hercules in his fighting form. (A quote from this section of the play is preserved in Dionysius of Halicarnassus' Roman Antiquities: "And thou shalt come to Liguria's dauntless host, Where no fault shalt thou find, bold though thou art, With the fray: 'tis fated thy missiles all shall fail.")
Ixion with his arms bound for trying to attack Juno.
Prometheus bound on Mount Caucasus.
The Scholia to Aratus mention three more mythical figures in connection with this constellation: Sisyphus or Tantalus, who suffered in Tartarus for having offended the gods, or Salmoneus, who was struck down by Zeus for his hubris. Another classical author associated the constellation with Atlas.
Equivalents
In Chinese astronomy, the stars that correspond to Hercules are located in two areas: the Purple Forbidden enclosure (紫微垣, Zǐ Wēi Yuán) and the Heavenly Market enclosure (天市垣, Tiān Shì Yuán).
Arab translators of Ptolemy named it in (not to be confused with ), the name for the star Mu Draconis.
Hence its Swahili name .
See also
Hercules (Chinese astronomy)
References
Further reading
H. A. Rey, The Stars — A New Way To See Them. Enlarged World-Wide Edition. Houghton Mifflin, Boston, 1997. .
Ian Ridpath and Wil Tirion (2007). Stars and Planets Guide, Collins, London. . Princeton University Press, Princeton. .
External links
The Deep Photographic Guide to the Constellations: Hercules
The clickable Hercules
Star Tales – Hercules
Warburg Institute Iconographic Database (ca 160 medieval and early modern images of Hercules)
Constellations
Northern constellations
Constellations listed by Ptolemy
Hercules | Hercules (constellation) | [
"Astronomy"
] | 3,689 | [
"Constellations listed by Ptolemy",
"Constellations",
"Northern constellations",
"Hercules (constellation)",
"Sky regions"
] |
362,598 | https://en.wikipedia.org/wiki/Indium%20tin%20oxide | Indium tin oxide (ITO) is a ternary composition of indium, tin and oxygen in varying proportions. Depending on the oxygen content, it can be described as either a ceramic or an alloy. Indium tin oxide is typically encountered as an oxygen-saturated composition with a formulation of 74% In, 8% Sn, and 18% O by weight. Oxygen-saturated compositions are so typical that unsaturated compositions are termed oxygen-deficient ITO. It is transparent and colorless in thin layers, while in bulk form it is yellowish to gray. In the infrared region of the spectrum it acts as a metal-like mirror.
Indium tin oxide is one of the most widely used transparent conducting oxides, not just for its electrical conductivity and optical transparency, but also for the ease with which it can be deposited as a thin film, as well as its chemical resistance to moisture. As with all transparent conducting films, a compromise must be made between conductivity and transparency, since increasing the thickness and increasing the concentration of charge carriers increases the film's conductivity, but decreases its transparency.
Thin films of indium tin oxide are most commonly deposited on surfaces by physical vapor deposition. Often used is electron beam evaporation, or a range of sputter deposition techniques.
Material and properties
ITO is a mixed oxide of indium and tin with a melting point in the range 1526–1926 °C (1800–2200 K, 2800–3500 °F), depending on composition. The most commonly used material is an oxide of a composition of ca. In4Sn. The material is a n-type semiconductor with a large bandgap of around 4 eV. ITO is both transparent to visible light and relatively conductive. It has a low electrical resistivity of ~10−4 Ω·cm, and a thin film can have an optical transmittance of greater than 80%. These properties are utilized to great advantage in touch-screen applications such as mobile phones.
Common uses
Indium tin oxide (ITO) is an optoelectronic material that is applied widely in both research and industry. ITO can be used for many applications, such as flat-panel displays, smart windows, polymer-based electronics, thin film photovoltaics, glass doors of supermarket freezers, and architectural windows. Moreover, ITO thin films for glass substrates can be helpful for glass windows to conserve energy.
ITO green tapes are utilized for the production of lamps that are electroluminescent, functional, and fully flexible. Also, ITO thin films are used primarily to serve as coatings that are anti-reflective and for liquid crystal displays (LCDs) and electroluminescence, where the thin films are used as conducting, transparent electrodes.
ITO is often used to make transparent conductive coating for displays such as liquid crystal displays, OLED displays, plasma displays, touch panels, and electronic ink applications. Thin films of ITO are also used in organic light-emitting diodes, solar cells, antistatic coatings and EMI shieldings. In organic light-emitting diodes, ITO is used as the anode (hole injection layer).
ITO films deposited on windshields are used for defrosting aircraft windshields. The heat is generated by applying a voltage across the film. ITO is also used to reflect electromagnetic radiation. The F-22 Raptor's canopy has an ITO coating that reflects radar waves, enhancing its stealth capabilities and giving it a distinctive gold tint.
ITO is also used for various optical coatings, most notably infrared-reflecting coatings (hot mirrors) for automotive, and sodium vapor lamp glasses. Other uses include gas sensors, antireflection coatings, electrowetting on dielectrics, and Bragg reflectors for VCSEL lasers. ITO is also used as the IR reflector for low-e window panes. ITO was also used as a sensor coating in the later Kodak DCS cameras, starting with the Kodak DCS 520, as a means of increasing blue channel response.
ITO thin film strain gauges can operate at temperatures up to 1400 °C and can be used in harsh environments, such as gas turbines, jet engines, and rocket engines.
Silver nanoparticle–ITO hybrid
ITO has been popularly used as a high-quality flexible substrate to produce flexible electronics. However, this substrate's flexibility decreases as its conductivity improves. Previous research have indicated that the mechanical properties of ITO can be improved through increasing the degree of crystallinity. Doping with silver (Ag) can improve this property, but results in a loss of transparency. An improved method that embeds Ag nanoparticles (AgNPs) instead of homogeneously to create a hybrid ITO has proven to be effective in compensating for the decrease in transparency. The hybrid ITO consists of domains in one orientation grown on the AgNPs and a matrix of the other orientation. The domains are stronger than the matrix and function as barriers to crack propagation, significantly increasing the flexibility. The change in resistivity with increased bending significantly decreases in the hybrid ITO compared with homogeneous ITO.
Alternative synthesis methods
ITO is typically deposited through expensive and energy-intensive processes that deal with physical vapor deposition (PVD). Such processes include sputtering, which results in the formation of brittle layers.
Because of the cost and energy of physical vapor deposition, with the required vacuum processing, alternative methods of preparing ITO are being investigated.
Tape casting process
An alternative process that uses a particle-based technique, is known as the tape casting process. Because it is a particle-based technique, the ITO nano-particles are dispersed first, then placed in organic solvents for stability. Benzyl phthalate plasticizer and polyvinyl butyral binder have been shown to be helpful in preparing nanoparticle slurries. Once the tape casting process has been carried out, the characterization of the green ITO tapes showed that optimal transmission went up to about 75%, with a lower bound on the electrical resistance of 2 Ω·cm.
Laser sintering
Using ITO nanoparticles imposes a limit on the choice of substrate, owing to the high temperature required for sintering. As an alternative starting material, In-Sn alloy nanoparticles allow for a more diverse range of possible substrates. A continuous conductive In-Sn alloy film is formed firstly, followed by oxidation to bring transparency. This two step process involves thermal annealing, which requires special atmosphere control and increased processing time. Because metal nanoparticles can be converted easily into a conductive metal film under the treatment of laser, laser sintering is applied to achieve products' homogeneous morphology. Laser sintering is also easy and less costly to use since it can be performed in air.
Ambient gas conditions
For example, using conventional methods but varying the ambient gas conditions to improve the optoelectronic properties as, for example, oxygen plays a major role in the properties of ITO.
Chemical shaving for very thin films
There has been numerical modeling of plasmonic metallic nanostructures have shown great potential as a method of light management in thin-film nanodisc-patterned hydrogenated amorphous silicon (a-Si:H) solar photovoltaic (PV) cells. A problem that arises for plasmonic-enhanced PV devices is the requirement for 'ultra-thin' transparent conducting oxides (TCOs) with high transmittance and low enough resistivity to be used as device top contacts/electrodes. Unfortunately, most work on TCOs is on relatively thick layers and the few reported cases of thin TCO showed a marked decrease in conductivity. To overcome this it is possible to first grow a thick layer and then chemically shave it down to obtain a thin layer that is whole and highly conductive.
Constraints and trade-offs
A major concern with ITO is its cost. ITO costs several times more than aluminium zinc oxide (AZO). AZO is a common choice of transparent conducting oxide (TCO) because of its lower cost and relatively good optical transmission performance in the solar spectrum. However, ITO is superior to AZO in many other important performance categories including chemical resistance to moisture. ITO is not affected by moisture, and is stable as part of copper indium gallium selenide solar cell for 25–30 years on a rooftop.
While the sputtering target or evaporative material that is used to deposit the ITO is significantly more costly than AZO, the amount of material placed on each cell is quite small. Therefore, the cost penalty per cell is quite small, too.
Benefits
The primary advantage of ITO compared to AZO as a transparent conductor for LCDs is that ITO can be precisely etched into fine patterns. AZO cannot be etched as precisely: It is so sensitive to acid that it tends to get over-etched by an acid treatment.
Another benefit of ITO compared to AZO is that if moisture does penetrate, ITO will degrade less than AZO.
The role of ITO glass as a cell culture substrate can be extended easily, which opens up new opportunities for studies on growing cells involving electron microscopy and correlative light.
Research examples
ITO can be used in nanotechnology to provide a path to a new generation of solar cells. Solar cells made with these devices have the potential to provide low-cost, ultra-lightweight, and flexible cells with a wide range of applications. Because of the nanoscale dimensions of the nanorods, quantum-size effects influence their optical properties. By tailoring the size of the rods, they can be made to absorb light within a specific narrow band of colors. By stacking several cells with different sized rods, a broad range of wavelengths across the solar spectrum can be collected and converted to energy. Moreover, the nanoscale volume of the rods leads to a significant reduction in the amount of semiconductor material needed compared to a conventional cell. Recent studies demonstrated that nanostructured ITO can behave as a miniaturized photocapacitor, combining in a unique material the absorption and storage of light energy.
Health and safety
Inhalation of indium tin oxide may cause mild irritation to the respiratory tracts and should be avoided. If exposure is long-term, symptoms may become chronic and result in benign pneumoconiosis. Studies with animals indicate that indium tin oxide is toxic when ingested, along with negative effects on the kidney, lung, and heart.
During the process of mining, production and reclamation, workers are potentially exposed to indium, especially in countries such as China, Japan, the Republic of Korea, and Canada and face the possibility of pulmonary alveolar proteinosis, pulmonary fibrosis, emphysema, and granulomas. Workers in the US, China, and Japan have been diagnosed with cholesterol clefts under indium exposure. Silver nanoparticles existed in improved ITOs have been found in vitro to penetrate through both intact and breached skin into the epidermal layer. Un-sintered ITOs are suspected of induce T-cell-mediated sensitization: on an intradermal exposure study, a concentration of 5% uITO resulted in lymphocyte proliferation in mice including the number increase of cells through a 10-day period.
A new occupational problem called indium lung disease was developed through contact with indium-containing dusts. The first patient is a worker associated with wet surface grinding of ITO who suffered from interstitial pneumonia: his lung was filled with ITO related particles. These particles can also induce cytokine production and macrophage dysfunction. Sintered ITOs particles alone can cause phagocytic dysfunction but not cytokine release in macrophage cells; however, they can intrigue a pro-inflammatory cytokine response in pulmonary epithelial cells. Unlike uITO, they can also bring endotoxin to workers handling the wet process if in contact with endotoxin-containing liquids. This can be attributed to the fact that sITOs have larger diameter and smaller surface area, and that this change after the sintering process can cause cytotoxicity.
Because of these issues, alternatives to ITO have been found.
Recycling
The etching water used in the process of sintering ITO can only be used for a limited numbers of times before it has to be disposed. After degradation, the waste water should still contain valuable metals such as In and Cu as a secondary resource as well as Mo, Cu, Al, Sn and In, which can pose a health hazard to human beings.
Alternative materials
Because of high cost and limited supply of indium, the fragility and lack of flexibility of ITO layers, and the costly layer deposition requiring vacuum, alternative materials are being investigated. Promising alternatives based on zinc oxide doped with various elements.
Doped compounds
Promising alternatives based on zinc oxide doped with various elements.
Several transition metal dopants in indium oxide, particularly molybdenum, give much higher electron mobility and conductivity than obtained with tin. Doped binary compounds such as aluminum-doped zinc oxide (AZO) and indium-doped cadmium oxide have been proposed as alternative materials. Other inorganic alternatives include aluminum, gallium or indium-doped zinc oxide (AZO, GZO or IZO).
Carbon nanotubes
Carbon nanotube conductive coatings are a prospective replacement.
Graphene
As another carbon-based alternative, films of graphene are flexible and have been shown to allow 90% transparency with a lower electrical resistance than standard ITO. Thin metal films are also seen as a potential replacement material. A hybrid material alternative currently being tested is an electrode made of silver nanowires and covered with graphene. The advantages to such materials include maintaining transparency while simultaneously being electrically conductive and flexible.
Conductive polymers
Inherently conductive polymers (ICPs) are also being developed for some ITO applications. Typically the conductivity is lower for conducting polymers, such as polyaniline and PEDOT:PSS, than for inorganic materials, but they are more flexible, less expensive and more environmentally friendly in processing and manufacture.
Amorphous indium–zinc oxide
In order to reduce indium content, decrease processing difficulty, and improve electrical homogeneity, amorphous transparent conducting oxides have been developed. One such material, amorphous indium-zinc-oxide maintains short-range order even though crystallization is disrupted by the difference in the ratio of oxygen to metal atoms between In2O3 and ZnO. Indium-zinc-oxide has some comparable properties to ITO. The amorphous structure remains stable even up to 500 °C, which allows for important processing steps common in organic solar cells. The improvement in homogeneity significantly enhances the usability of the material in the case of organic solar cells. Areas of poor electrode performance in organic solar cells render a percentage of the cell's area unusable.
See also
Transparent conducting film
References
External links
Spectroscopic studies of conducting metal oxides, with many slides about ITO
Articles containing unverified chemical infoboxes
Oxides
Indium compounds
Tin
Display technology
Transparent electrodes | Indium tin oxide | [
"Chemistry",
"Engineering"
] | 3,094 | [
"Electronic engineering",
"Oxides",
"Display technology",
"Salts"
] |
362,605 | https://en.wikipedia.org/wiki/Poa%20pratensis | Poa pratensis, commonly known as Kentucky bluegrass (or blue grass), smooth meadow-grass, or common meadow-grass, is a perennial species of grass native to practically all of Europe, North Asia and the mountains of Algeria and Morocco. There is disagreement about its native status in North America, with some sources considering it native and others stating the Spanish Empire brought the seeds of Kentucky bluegrass to the New World in mixtures with other grasses. It is a common and incredibly popular lawn grass in North America with the species being spread over all of the cool, humid parts of the United States. In its native range, Poa pratensis forms a valuable pasture plant, characteristic of well-drained, fertile soil. It is also used for making lawns in parks and gardens and has established itself as a common invasive weed across cool moist temperate climates like the Pacific Northwest and the Northeastern United States. When found on native grasslands in Canada, for example, it is considered an unwelcome exotic plant, and is indicative of a disturbed and degraded landscape.
Taxonomy
Poa pratensis was one of the many species described by Carl Linnaeus in his landmark work Species Plantarum in 1753. is Greek for fodder and pratensis is derived from , the Latin for meadow. The name Kentucky bluegrass derives from its flower heads, which are blue when the plant is allowed to grow to its natural height of .
Poa pratensis is the type species of the grass family Poaceae.
There are two ill-defined subspecies:
Poa pratensis subsp. pratensis – temperate regions
Poa pratensis subsp. colpodea – Arctic
Description
Poa pratensis is a herbaceous perennial plant tall. The leaves have boat-shaped tips, narrowly linear, up to long and broad, smooth or slightly roughened, with a rounded to truncate ligule long. The conical panicle is long, with 3 to 5 branches in the basal whorls; the oval spikelets are long with 2 to 5 florets, and are purplish-green or grey. They are in flower from May to July, compared to annual meadowgrass (Poa annua) which is in flower for eight months of the year. Poa pratensis has a fairly prominent mid-vein (center of the blade).
The ligule is extremely short and square-ended, making a contrast with annual meadowgrass (Poa annua) and rough meadowgrass (Poa trivialis) in which it is silvery and pointed. The Kentucky bluegrass is a dark green/blue compared to the apple-green color of Poa annua and Poa trivialis.
The rootstock is creeping, with runners (rhizomes). The broad, blunt leaves tend to spread at the base, forming close mats.
Ecology
Poa pratensis is among the food plants of the caterpillars of the meadow brown (Maniola jurtina), gatekeeper (Pyronia tithonus), and pepper-and-salt skipper butterflies; the common sun beetle (Amara aenea) (adults feed on the developing seeds), Eupelix cuspidata of the leafhopper family, and Myrmus miriformis, a grassbug (feeds on young blades and developing seeds).
Poa pratensis is host to a number of fungi, including Claviceps purpurea, which causes ergotism when consumed, Drechslera poae, Epichloë typhina, Phaeoseptoria poae, Puccinia brachypodii var. poae-nemoralis, Stagonospora montagnei, Stagonospora nodorum and Wojnowicia hirta.
Cultivation and production
The Central Kentucky Blue Grass Seed Company Building is on the National Register of Historic Places. Since the 1950s and early 1960s, 90% of Kentucky bluegrass seed in the United States has been produced on specialist farms in Idaho, Oregon and Washington.
During the 1990s botanists began experimenting with hybrids of Poa pratensis and Texas bluegrass (P. arachnifera), with the goal of creating a drought and heat-resistant lawn grass. In warm climates, such hybrids may remain green year-round.
Bella Bluegrass is a brand-named dwarf variant of Poa pratentis developed by the University of Nebraska. It has relatively deep roots and propagates relatively rapidly horizontally from its root system but grows to only in above-ground height, basically eliminating the need for mowing lawns that use it. It cannot be reproduced by seed and thus depends on sod plugs or sprigging for its production.
NFL playing surfaces
Cleveland Browns Stadium in Cleveland, Ohio
Empower Field at Mile High in Denver, Colorado
Acrisure Stadium in Pittsburgh, Pennsylvania
MLB playing surfaces
Yankee Stadium in Bronx, New York
Oriole Park at Camden Yards in Baltimore, Maryland
Progressive Field in Cleveland, Ohio
Angel Stadium in Anaheim, California
Busch Stadium in St. Louis, Missouri
Citizens Bank Park in Philadelphia, Pennsylvania
American Family Field in Milwaukee, Wisconsin
Nationals Park in Washington, D.C.
Citi Field in Queens, New York
Comerica Park in Detroit, Michigan
Guaranteed Rate Field in Chicago, Illinois
Target Field in Minneapolis, Minnesota
PNC Park in Pittsburgh, Pennsylvania
Fenway Park in Boston, Massachusetts
Oakland Coliseum in Oakland, California
Coors Field in Denver, Colorado (Kentucky Bluegrass/Perennial Ryegrass Blend)
T-Mobile Park in Seattle, Washington (Kentucky Bluegrass/Perennial Ryegrass Blend)
Great American Ball Park in Cincinnati, Ohio (Kentucky Bluegrass Blend)
Wrigley Field in Chicago, Illinois (Kentucky Bluegrass/Clover Blend)
Kauffman Stadium in Kansas City, Missouri (Kentucky Bluegrass/Perennial Ryegrass Blend)
Gallery
References
Further reading
Flora Europaea: Poa pratensis
European Poa Database
Horticultural information on this turfgrass; growing it in the home garden * The Observers Book of Grasses, Sedges and Rushes. Frances Rose. pages 42–43
PennState Extension Kentucky Bluegrass Facts and Identification
Kew gardens grass database
External links
Cosmopolitan species
Grasses of Africa
Grasses of Asia
Grasses of Europe
Grasses of North America
Lawn grasses
Plants described in 1753
pratensis
Taxa named by Carl Linnaeus
Grasses of Lebanon | Poa pratensis | [
"Biology"
] | 1,279 | [
"Cosmopolitan species",
"Organisms by location"
] |
362,612 | https://en.wikipedia.org/wiki/Ludolph%20van%20Ceulen | Ludolph van Ceulen (, ; 28 January 1540 – 31 December 1610) was a German-Dutch mathematician from Hildesheim. He immigrated to the Netherlands.
Biography
Van Ceulen moved to Delft most likely in 1576 to teach fencing and mathematics and in 1594 opened a fencing school in Leiden. In 1600 he was appointed the first professor of mathematics at the Engineering School, Duytsche Mathematique, established by Maurice, Prince of Orange, at the relatively new Leiden University. He shared this professorial level at the school with the surveyor and cartographer, , which shows that the intention was to promote practical, rather than theoretical instruction.
The curriculum for the new Engineering School was devised by Simon Stevin who continued to act as the personal advisor to the Prince. At first the professors at Leiden refused to accept the status of Van Ceulen and Van Merwen, especially as they taught in Dutch rather than Latin. Theological professors generally believed that practical courses were not acceptable studies for a university, but they were not willing to reject the School outright since it was founded by Prince Maurice.
Leiden University governors heard in April 1600 that Adriaan Metius, a fortification advisor to Prince Maurice and the States General, had been recruited and raised to the level of a full professor to teach mathematics at the rival Franeker University. The Leiden governors' main problem was to match Franeker University, without raising the status too much of Duytsche Mathematique. So they quickly recruited mathematician Rudolf Snellius to the university—as distinct from the Engineering School—but then relegated him to the Faculty of Arts.
When the first degrees were to be conferred on Engineering School graduates in 1602 (under protest from the University) the governors and University's senate refused to award them except via an examination conducted by the Universities' own mathematics professor, Rudolf Snellius—ensuring that Van Ceulen and Van Merwen were seen as inferior to the university's own mathematician.
However Rudolf Snellius and his son Willebrord Snellius (the formulator of Snell's law—who replaced his father) both taught mathematics at Leiden University and appear to have cooperated closely with Van Ceulen, Van Merwen, Simon Stevin and the Engineering School. Willebrord Snellius, in fact, worked closely with Stevin.
Van Ceulen died in Leiden in 1610.
Calculating
Ludolph van Ceulen spent a major part of his life calculating the numerical value of the mathematical constant , using essentially the same methods as those employed by Archimedes some seventeen hundred years earlier. He published a 20-decimal value in his 1596 book Van den Circkel ("On the Circle"), which was published before he moved to Leiden, and he later expanded this to 35 decimals.
Van Ceulen's 20 digits is more than enough precision for any conceivable practical purpose. Even if a circle was perfect down to the atomic scale, the thermal vibrations of the molecules of ink would make most of those digits physically meaningless. Future attempts to calculate to ever greater precision have been driven primarily by curiosity about the number itself.
Legacy
After his death, the "Ludolphine number",
3.14159265358979323846264338327950288...,
was engraved on his tombstone in Leiden. The tombstone was eventually lost, but later restored in 2000.
His book "De circulo & adscriptis liber" was translated into Latin after his death by Snellius.
In Germany, is still sometimes referred to as the "Ludolphine number".
See also
Area of a circle
References
External links
"Digits of Pi" by Barry Arthur Cipra (includes photo of tombstone)
Oomes, R. M. Th. E.; Tersteeg, J. J. T. M.; Top, J. "The epitaph of Ludolph van Ceulen." Nieuw Arch. Wiskd. (5) 1 (2000), no. 2. online
Ludolph van Ceulen (1596) Vanden circkel - Linda Hall Library
Ludolph van Ceulen (1619) De circulo et adscriptis liber and Surdorum quadraticorum arithmetica - Linda Hall Library
1540 births
1610 deaths
16th-century Dutch mathematicians
17th-century Dutch mathematicians
16th-century German mathematicians
Academic staff of Leiden University
People from Hildesheim
Pi-related people
Burials at Pieterskerk, Leiden | Ludolph van Ceulen | [
"Mathematics"
] | 947 | [
"Pi-related people",
"Pi"
] |
362,631 | https://en.wikipedia.org/wiki/Bar%20%28unit%29 | The bar is a metric unit of pressure defined as 100,000 Pa (100 kPa), though not part of the International System of Units (SI). A pressure of 1 bar is slightly less than the current average atmospheric pressure on Earth at sea level (approximately 1.013 bar). By the barometric formula, 1 bar is roughly the atmospheric pressure on Earth at an altitude of 111 metres at 15 °C.
The bar and the millibar were introduced by the Norwegian meteorologist Vilhelm Bjerknes, who was a founder of the modern practice of weather forecasting, with the bar defined as one megadyne per square centimeter.
The SI brochure, despite previously mentioning the bar, now omits any mention of it. The bar has been legally recognised in countries of the European Union since 2004. The US National Institute of Standards and Technology (NIST) deprecates its use except for "limited use in meteorology" and lists it as one of several units that "must not be introduced in fields where they are not presently used". The International Astronomical Union (IAU) also lists it under "Non-SI units and symbols whose continued use is deprecated".
Units derived from the bar include the megabar (symbol: Mbar), kilobar (symbol: kbar), decibar (symbol: dbar), centibar (symbol: cbar), and millibar (symbol: mbar).
Definition and conversion
The bar is defined using the SI derived unit, pascal: ≡ 100,000 Pa ≡ 100,000 N/m2.
Thus, is equal to:
1,000,000 Ba (barye) (in cgs units);
and 1 bar is approximately equal to:
1019.716 centimetres of water (cmH2O) (1 bar approximately corresponds to the gauge pressure of water at a depth of 10 meters).
1 millibar (mbar) is equal to:
(0.001 bar)
.
Origin
The word bar has its origin in the Ancient Greek word (), meaning weight. The unit's official symbol is bar; the earlier symbol b is now deprecated and conflicts with the uses of b denoting the unit barn or bit, but it is still encountered, especially as mb (rather than the proper mbar) to denote the millibar. Between 1793 and 1795, the word bar was used for a unit of mass (equal to the modern tonne) in an early version of the metric system.
Usage
Atmospheric air pressure where standard atmospheric pressure is defined as 1013.25 mbar, 101.325 kPa, 1.01325 bar, which is about . Despite the millibar not being an SI unit, meteorologists and weather reporters worldwide have long measured air pressure in millibar as the values are convenient. After the advent of SI units, some meteorologists began using hectopascals (symbol hPa) which are numerically equivalent to millibar; for the same reason, the hectopascal is now the standard unit used to express barometric pressures in aviation in most countries. For example, the weather office of Environment Canada uses kilopascals and hectopascals on their weather maps. In contrast, Americans are familiar with the use of the millibar in US reports of hurricanes and other cyclonic storms.
In fresh water, there is an approximate numerical equivalence between the change in pressure in decibar and the change in depth from the water surface in metres. Specifically, an increase of 1 decibar occurs for every 1.019716 m increase in depth. In sea water with respect to the gravity variation, the latitude and the geopotential anomaly the pressure can be converted into metres' depth according to an empirical formula (UNESCO Tech. Paper 44, p. 25). As a result, decibar is commonly used in oceanography.
In scuba diving, bar is also the most widely used unit to express pressure, e.g. 200 bar being a full standard scuba tank, and depth increments of 10 metre of seawater being equivalent to 1 bar of pressure.
Many engineers worldwide use the bar as a unit of pressure because, in much of their work, using pascals would involve using very large numbers. In measurement of vacuum and in vacuum engineering, residual pressures are typically given in millibar, although torr or millimeter of mercury (mmHg) were historically common.
Pressures resulting from deflagrations are often expressed in units of bar.
In the automotive field, turbocharger boost is often described in bar outside the United States. Tire pressure is often specified in bar. In hydraulic machinery components are rated to the maximum system oil pressure, which is typically in hundreds of bar. For example, 300 bar is common for industrial fixed machinery.
In the maritime ship industries, pressures in piping systems, such as cooling water systems, is often measured in bar.
Unicode has characters for "mb" (), "bar" () and (; "millibar" spelt in katakana), but they exist only for compatibility with legacy Asian encodings and are not intended to be used in new documents.
The kilobar, equivalent to 100 MPa, is commonly used in geological systems, particularly in experimental petrology.
The abbreviations "bar(a)" and "bara" are sometimes used to indicate absolute pressures, and "bar(g)" and "barg" for gauge pressures. The usage is deprecated but still prevails in the oil industry (often by capitalized "BarG" and "BarA"). As gauge pressure is relative to the current ambient pressure, which may vary in absolute terms by about 50 mbar, "BarG" and "BarA" are not interconvertible. Fuller descriptions such as "gauge pressure of 2 bars" or "2-bar gauge" are recommended.
See also
Centimetre or millimetre of water
List of metric units
Metric prefix
References
External links
Official SI website: Table 8. Non-SI units accepted for use with the SI
US government atmospheric pressure map showing atmospheric pressure in mbar
Units of pressure
Non-SI metric units | Bar (unit) | [
"Mathematics"
] | 1,274 | [
"Non-SI metric units",
"Quantity",
"Units of measurement",
"Units of pressure"
] |
362,635 | https://en.wikipedia.org/wiki/Kazimierz%20Zarankiewicz | Kazimierz Zarankiewicz (2 May 1902 – 5 September 1959) was a Polish mathematician and Professor at the Warsaw University of Technology who was interested primarily in topology and graph theory.
Biography
Zarankiewicz was born in Częstochowa, to father Stanisław and mother Józefa (née Borowska). He studied at the University of Warsaw, together with Zygmunt Janiszewski, Stefan Mazurkiewicz, Wacław Sierpiński, Kazimierz Kuratowski, and Stanisław Saks.
During World War II, Zarankiewicz took part in illegal teaching, forbidden by the German authorities, and was eventually sent to a concentration camp. He survived and became a teacher at Warsaw University of Technology (Polish: Politechnika Warszawska).
He visited universities in Tomsk, Harvard, London, and Vienna. He served as president of the Warsaw section of the Polish Mathematical Society and the International Astronautical Federation.
He died in London, England.
Research contributions
Zarankiewicz wrote works on cut-points in connected spaces, on conformal mappings, on complex functions and number theory, and triangular numbers.
The Zarankiewicz problem is named after Zarankiewicz. This problem asks, for a given size of (0,1)-matrix, how many matrix entries must be set equal to 1 in order to guarantee that the matrix contains at least one a × b submatrix is made up only of 1's. An equivalent formulation in extremal graph theory asks for the maximum number of edges in a bipartite graph with no complete bipartite subgraph Ka,b.
The Zarankiewicz crossing number conjecture in the mathematical field of graph theory is also named after Zarankiewicz. The conjecture states that the crossing number of a complete bipartite graph equals
Zarankiewicz proved that this formula is an upper bound for the actual crossing number. The problem of determining the number was suggested by Paul Turán and became known as Turán's brick factory problem.
See also
List of Polish mathematicians
References
External links
20th-century Polish mathematicians
Topologists
University of Warsaw alumni
Academic staff of the Warsaw University of Technology
Nazi concentration camp survivors
People from Częstochowa
1902 births
1959 deaths | Kazimierz Zarankiewicz | [
"Mathematics"
] | 469 | [
"Topologists",
"Topology"
] |
362,649 | https://en.wikipedia.org/wiki/Stanis%C5%82aw%20Saks | Stanisław Saks (30 December 1897 – 23 November 1942) was a Polish mathematician and university tutor, a member of the Lwów School of Mathematics, known primarily for his membership in the Scottish Café circle, an extensive monograph on the theory of integrals, his works on measure theory and the Vitali–Hahn–Saks theorem.
Life and work
Stanisław Saks was born on 30 December 1897 in Kalisz, Congress Poland, to an assimilated Polish-Jewish family. In 1915 he graduated from a local gymnasium and joined the newly recreated Warsaw University. In 1922 he received a doctorate of his alma mater with a prestigious distinction maxima cum laude. Soon afterwards he also passed his habilitation and received the Rockefeller fellowship, which allowed him to travel to the United States. Around that time he started publishing articles in various mathematical journals, mostly the Fundamenta Mathematicae, but also in the Transactions of the American Mathematical Society. He participated in the Silesian Uprisings and was awarded the Cross of the Valorous and the Medal of Independence for his bravery. Following the end of the uprising he returned to Warsaw and resumed his academic career.
For most of it he studied the theories of functions and functionals in particular. In 1930 he published his most notable book, the Zarys teorii całki (Sketch on the Theory of the Integral), which later got expanded and translated into several languages, including English (Theory of the Integral), French (Théorie de l'Intégrale) and Russian (Teoriya Integrala). Despite his successes, Saks was never awarded the title of professor and remained an ordinary tutor, initially at his alma mater and the Warsaw University of Technology, and later at the Lwów University and Wilno University. He was also an active socialist and a journalist at the Robotnik weekly (1919–1926) and later a collaborator of the Association of Socialist Youth.
Saks wrote a mathematics book with Antoni Zygmund, Analytic Functions, in 1933. It was translated into English in 1952 by E. J. Scott. In the preface to the English edition, Zygmund writes:
Stanislaw Saks was a man of moral as well as physical courage, of rare intelligence and wit. To his colleagues and pupils he was an inspiration not only as a mathematician but as a human being. In the period between the two world wars he exerted great influence upon a whole generation of Polish mathematicians in Warsaw and Lwów. In November 1942, at the age of 45, Saks died in a Warsaw prison, victim of a policy of extermination.
After the outbreak of World War II and the occupation of Poland by Germany, Saks joined the Polish underground. Arrested in November 1942, he was executed on 23 November 1942 by the German Gestapo in Warsaw.
Publications
. English translation by Laurence Chisholm Young, with two additional notes by Stefan Banach.
See also
Lwów School of Mathematics
Notes
References
Functional analysts
Measure theorists
1897 births
1942 deaths
Lwów School of Mathematics
Mathematical analysts
University of Warsaw alumni
People from Kalisz
Academic staff of Vilnius University
Polish Jews who died in the Holocaust
Warsaw School of Mathematics | Stanisław Saks | [
"Mathematics"
] | 646 | [
"Mathematical analysis",
"Mathematical analysts"
] |
362,677 | https://en.wikipedia.org/wiki/Rock%20candy | Rock candy or sugar candy, also called rock sugar, or crystal sugar, is a type of confection composed of relatively large sugar crystals. In some parts of the world, local variations are called Misri, nabat or navat.
This candy is formed by allowing a supersaturated solution of sugar and water to crystallize onto a surface suitable for crystal nucleation, such as a string, stick, or plain granulated sugar. Heating the water before adding the sugar allows more sugar to dissolve thus producing larger crystals. Crystals form after six to seven days. Food coloring may be added to the mixture to produce colored candy.
Nomenclature
Etymologically, "sugar candy" derives from late 13th century English (in reference to "crystallized sugar"), from Old French çucre candi (meaning "sugar candy"), and ultimately from Arabic qandi, from Persian qand ("cane sugar"), probably from Sanskrit khanda ("piece of sugar)", The sense gradually broadened (especially in the United States) to mean by the late 19th century "any confection having sugar as its basis". In Britain, these are sweets, and "candy" tends to be restricted to sweets made only from boiled sugar and striped in bright colors.
The modern American term "rock candy" (referring to brittle large natural sugar crystals) should not be confused with the British term rock (referring to an amorphous and opaque boiled sugar product, initially hard but then chewy at mouth temperature).
Origins
Islamic writers in the first half of the 9th century described the production of candy sugar, where crystals were grown through cooling supersaturated sugar solutions. One of the famed makers of rock candy in the Muslim east is Hafiz Mustafa in 1864 in Istanbul founded during the reign of Sultan Abdulaziz.
According to the production process, rock sugar is divided into two types: single crystal rock sugar and polycrystalline rock sugar.
Cuisine
Rock candy is often dissolved in tea. It is an important part of the tea culture of East Frisia, where a lump of rock sugar is placed at the bottom of the cup. Rock candy consumed with tea is also the most common and popular way of drinking tea in Iran, where it is called nabat; the most popular nabat flavor is saffron. This method of drinking tea can also be found in Central Asia as novvot.
It is a common ingredient in Chinese cooking. In China, it is used to sweeten chrysanthemum tea, as well as Cantonese dessert soups and the liquor baijiu. Many households have rock candy available to marinate meats, add to stir fry, and to prepare food such as yao shan. In less modern times, rock sugar was a luxury only for the wealthy. Rock candy is also regarded as having medicinal properties, and in some Chinese provinces, it is used as a part of traditional Chinese medicine.
Rock candy is used a lot in other countries. In Mexico, it is used during the Day of the Dead to make sugar skulls, often highly decorated. Sugar skulls are given to children so they will not fear death; they are also offered to the dead. In the Friesland province of the Netherlands, bits of rock candy are baked in the luxury white bread Fryske Sûkerbôle. Rock candy is a common ingredient in Tamil cuisine, particularly in the Sri Lankan city of Jaffna. In the US, rock candy comes in many colors and flavors, and is slightly hard to find, due to it being considered old-fashioned.
Misri
Misri refers to crystallized sugar lumps, and a type of confectionery mineral, which has its origins in India and Iran, also known as rock sugar elsewhere. It is used in India as a type of candy, or used to sweeten milk or tea.
Among Indian misri dishes are mishri-mawa (kalakand), mishri-peda, which are more commonly eaten in Northern-Western India, Uttar Pradesh, Delhi, Rajasthan, Punjab, Odisha,
Gujarat, North coastal of Andhra Pradesh and many other states and parts of India.
The Ghantewala Halwai of Delhi, who started his career by selling Misri mawa in 1790 is famous for Misari mawa and sells 40 varieties of sweets made from Misari.
Beverages
Rock and rye is a term used both for alcoholic liqueurs and cocktails using rye whiskey and rock candy, as well as for non-alcoholic beverages made in imitation thereof, such as the "Rock & Rye" flavor of soda pop made by Faygo.
See also
Hard candy
Konpeitō
Jaggery, an early form of sugar
References
Further reading
External links
– an educational exercise in crystal and candy making (it may vary on however you want to make it).
Candy
Crystals
Types of sugar | Rock candy | [
"Chemistry",
"Materials_science"
] | 992 | [
"Crystallography",
"Crystals"
] |
362,718 | https://en.wikipedia.org/wiki/W%C5%82adys%C5%82aw%20Orlicz | Władysław Roman Orlicz (May 24, 1903 – August 9, 1990) was a Polish mathematician of Lwów School of Mathematics. His main interests were functional analysis and topology: Orlicz spaces are named after him.
Education and career
Orlicz was the third of Franciszek and Maria Orlicz's five children. His youngest brother died in the Polish-Soviet War, the eldest perished in the Stutthof concentration camp. The other brothers also became professors. The family moved several times. Orlicz attended school in Tarnów, Znojmo, and Lwów, where he finished school in 1920 and began studying mathematics at the Lwów Polytechnic University. He studied with Hugo Steinhaus, Antoni Łomnicki and Stanisław Ruziewicz, among others. As early as 1923 he took on small tasks at the Faculty of Mathematics. On August 1, 1925 he became a junior assistant at the Jan Kazimierz University in Lwów (now University of Lviv). He published his first scientific work in 1926 at the age of 23. In 1928 he completed his dissertation on the theory of orthogonal sequences. In 1929 he went to University of Göttingen on a scholarship and returned to Lemberg in 1930 as a senior assistant. In 1934 he presented his habilitation thesis The investigations of orthogonal systems. The following year he became an assistant professor at the Lwów Polytechnic University and received his teaching license at the University of Lwów. In 1937, he became an associate professor at the University of Poznań.
The outbreak of the Second World War surprised him while he was on vacation in Lemberg. Since he could not return to Poznań, he was appointed professor in Lemberg. Officially he worked as a teacher. When it became clear in early 1945 that Lemberg would no longer belong to Poland, Orlicz went back to Poznań. In 1948 he was appointed full professor at the University of Poznań, where he remained until his retirement in 1970. He also worked at the State Institute of Mathematics, which was incorporated into the Polish Academy of Sciences in 1952.
Orlicz was awarded the Stefan Banach Prize by the Polish Mathematical Society in 1948.
See also
Orlicz space
Orlicz–Pettis theorem
List of Polish mathematicians
External links
References
1903 births
1990 deaths
Lwów School of Mathematics
Functional analysts
Topologists
Recipients of the State Award Badge (Poland)
People from Brzesko County
Lviv Polytechnic alumni
Academic staff of Adam Mickiewicz University in Poznań
Academic staff of Lviv Polytechnic
Academic staff of the University of Lviv
20th-century Polish mathematicians
Recipients of the Medal of the 10th Anniversary of the People's Republic of Poland | Władysław Orlicz | [
"Mathematics"
] | 541 | [
"Topologists",
"Topology"
] |
362,722 | https://en.wikipedia.org/wiki/Heat%20death%20of%20the%20universe | The heat death of the universe (also known as the Big Chill or Big Freeze) is a hypothesis on the ultimate fate of the universe, which suggests the universe will evolve to a state of no thermodynamic free energy, and will therefore be unable to sustain processes that increase entropy. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work. In the language of physics, this is when the universe reaches thermodynamic equilibrium.
If the curvature of the universe is hyperbolic or flat, or if dark energy is a positive cosmological constant, the universe will continue expanding forever, and a heat death is expected to occur, with the universe cooling to approach equilibrium at a very low temperature after a long time period.
The hypothesis of heat death stems from the ideas of Lord Kelvin who, in the 1850s, took the theory of heat as mechanical energy loss in nature (as embodied in the first two laws of thermodynamics) and extrapolated it to larger processes on a universal scale. This also allowed Kelvin to formulate the heat death paradox, which disproves an infinitely old universe.
Origins of the idea
The idea of heat death stems from the second law of thermodynamics, of which one version states that entropy tends to increase in an isolated system. From this, the hypothesis implies that if the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, according to this hypothesis, there is a tendency in nature towards the dissipation (energy transformation) of mechanical energy (motion) into thermal energy; hence, by extrapolation, there exists the view that, in time, the mechanical movement of the universe will run down as work is converted to heat because of the second law.
The conjecture that all bodies in the universe cool off, eventually becoming too cold to support life, seems to have been first put forward by the French astronomer Jean Sylvain Bailly in 1777 in his writings on the history of astronomy and in the ensuing correspondence with Voltaire. In Bailly's view, all planets have an internal heat and are now at some particular stage of cooling. Jupiter, for instance, is still too hot for life to arise there for thousands of years, while the Moon is already too cold. The final state, in this view, is described as one of "equilibrium" in which all motion ceases.
The idea of heat death as a consequence of the laws of thermodynamics, however, was first proposed in loose terms beginning in 1851 by Lord Kelvin (William Thomson), who theorized further on the mechanical energy loss views of Sadi Carnot (1824), James Joule (1843) and Rudolf Clausius (1850). Thomson's views were then elaborated over the next decade by Hermann von Helmholtz and William Rankine.
History
The idea of the heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851, Lord Kelvin outlined the view, as based on recent experiments on the dynamical theory of heat: "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."
In 1852, Thomson published On a Universal Tendency in Nature to the Dissipation of Mechanical Energy, in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will naturally tend to dissipate or run down. The ideas in this paper, in relation to their application to the age of the Sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject. In 1862, Thomson published "On the age of the Sun's heat", an article in which he reiterated his fundamental beliefs in the indestructibility of energy (the first law) and the universal dissipation of energy (the second law), leading to diffusion of heat, cessation of useful motion (work), and exhaustion of potential energy, "lost irrecoverably" through the material universe, while clarifying his view of the consequences for the universe as a whole. Thomson wrote:
The clock's example shows how Kelvin was unsure whether the universe would eventually achieve thermodynamic equilibrium. Thompson later speculated that restoring the dissipated energy in "vis viva" and then usable work – and therefore revert the clock's direction, resulting in a "rejuvenating universe" – would require "a creative act or an act possessing similar power". Starting from this publication, Kelvin also introduced the heat death paradox (Kelvin's paradox), which challenged the classical concept of an infinitely old universe, since the universe has not achieved its thermodynamic equilibrium, thus further work and entropy production are still possible. The existence of stars and temperature differences can be considered an empirical proof that the universe is not infinitely old.
In the years to follow both Thomson's 1852 and the 1862 papers, Helmholtz and Rankine both credited Thomson with the idea, along with his paradox, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a "heat death" (Helmholtz), which will be the "end of all physical phenomena" (Rankine).
Current status
Proposals about the final state of the universe depend on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a hypothesized "open" or "flat" universe that continues expanding indefinitely, either a heat death or a Big Rip is expected to eventually occur. If the cosmological constant is zero, the universe will approach absolute zero temperature over a very long timescale. However, if the cosmological constant is positive, the temperature will asymptote to a non-zero positive value, and the universe will approach a state of maximum entropy in which no further work is possible.
Time frame for heat death
The theory suggests that from the "Big Bang" through the present day, matter and dark matter in the universe are thought to have been concentrated in stars, galaxies, and galaxy clusters, and are presumed to continue to do so well into the future. Therefore, the universe is not in thermodynamic equilibrium, and objects can do physical work.:§VID The decay time for a supermassive black hole of roughly 1 galaxy mass (1011 solar masses) because of Hawking radiation is in the order of 10100 years, so entropy can be produced until at least that time. Some large black holes in the universe are predicted to continue to grow up to perhaps 1014 during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10106 years. After that time, the universe enters the so-called Dark Era and is expected to consist chiefly of a dilute gas of photons and leptons.:§VIA With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long timescales. Speculatively, it is possible that the universe may enter a second inflationary epoch, or assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state.:§VE It is also possible that entropy production will cease and the universe will reach heat death.:§VID
It is suggested that, over vast periods of time, a spontaneous entropy decrease would eventually occur via the Poincaré recurrence theorem, thermal fluctuations, and fluctuation theorem. Through this, another universe could possibly be created by random quantum fluctuations or quantum tunnelling in roughly years.
Opposing views
Max Planck wrote that the phrase "entropy of the universe" has no meaning because it admits of no accurate definition. In 2008, Walter Grandy wrote: "It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence." According to László Tisza, "If an isolated system is not in equilibrium, we cannot associate an entropy with it." Hans Adolf Buchdahl writes of "the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system". According to Giovanni Gallavotti, "there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state". Discussing the question of entropy for non-equilibrium states in general, Elliott H. Lieb and Jakob Yngvason express their opinion as follows: "Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way." In Peter Landsberg's opinion: "The third misconception is that thermodynamics, and in particular, the concept of entropy, can without further enquiry be applied to the whole universe. ... These questions have a certain fascination, but the answers are speculations."
A 2010 analysis of entropy states, "The entropy of a general gravitational field is still not known", and "gravitational entropy is difficult to quantify". The analysis considers several possible assumptions that would be needed for estimates and suggests that the observable universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor. Lee Smolin goes further: "It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. ... Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems." This point of view is also supported by the fact of a recent experimental discovery of a stable non-equilibrium steady state in a relatively simple closed system. It should be expected that an isolated system fragmented into subsystems does not necessarily come to thermodynamic equilibrium and remain in non-equilibrium steady state. Entropy will be transmitted from one subsystem to another, but its production will be zero, which does not contradict the second law of thermodynamics.
In popular culture
In Isaac Asimov's 1956 short story The Last Question, humans repeatedly wonder how the heat death of the universe can be avoided.
In the 1981 Doctor Who story "Logopolis", the Doctor realizes that the Logopolitans have created vents in the universe to expel heat build-up into other universes—"Charged Vacuum Emboitments" or "CVE"—to delay the demise of the universe. The Doctor unwittingly travelled through such a vent in "Full Circle".
In the 1995 computer game I Have No Mouth, and I Must Scream, based on Harlan Ellison's short story of the same name, it is stated that AM, the malevolent supercomputer, will survive the heat death of the universe and continue torturing its immortal victims to eternity.
In the 2011 anime series Puella Magi Madoka Magica, the antagonist Kyubey reveals he is a member of an alien race who has been creating magical girls for millennia in order to harvest their energy to combat entropy and stave off the heat death of the universe.
In the last act of Final Fantasy XIV: Endwalker, the player encounters an alien race known as the Ea who have lost all hope in the future and any desire to live further, all because they have learned of the eventual heat death of the universe and see everything else as pointless due to its probable inevitability.
The overarching plot of the Xeelee Sequence concerns the Photino Birds' efforts to accelerate the heat death of the universe by accelerating the rate at which stars become white dwarves.
The 2019 hit indie video game Outer Wilds has several themes grappling with the idea of the heat death of the universe, and the theory that the universe is a cycle of big bangs once the previous one has experienced a heat death.
In "Singularity Immemorial", the seventh main story event of the mobile game Girls' Frontline: Neural Cloud, the plot is about a virtual sector made to simulate space exploration and the threat of the heat death of the universe. The simulation uses an imitation of Neural Cloud's virus entities known as the Entropics as a stand in for the effects of a heat death.
See also
References
Ultimate fate of the universe
Thermodynamic entropy
1851 in science | Heat death of the universe | [
"Physics"
] | 2,685 | [
"Statistical mechanics",
"Entropy",
"Physical quantities",
"Thermodynamic entropy"
] |
362,728 | https://en.wikipedia.org/wiki/Negative%20temperature | Certain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This phenomenon was first discovered at the University of Alberta. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system. A standard example of such a system is population inversion in laser physics.
Thermodynamic systems with unbounded phase space cannot achieve negative temperatures: adding heat always increases their entropy. The possibility of a decrease in entropy as energy increases requires the system to "saturate" in entropy. This is only possible if the number of high energy states is limited. For a system of ordinary (quantum or classical) particles such as atoms or dust, the number of high energy states is unlimited (particle momenta can in principle be increased indefinitely). Some systems, however (see the examples below), have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease.
History
The possibility of negative temperatures was first predicted by Lars Onsager in 1949.
Onsager was investigating 2D vortices confined within a finite area, and realized that since their positions are not independent degrees of freedom from their momenta, the resulting phase space must also be bounded by the finite area. Bounded phase space is the essential property that allows for negative temperatures, and can occur in both classical and quantum systems. As shown by Onsager, a system with bounded phase space necessarily has a peak in the entropy as energy is increased. For energies exceeding the value where the peak occurs, the entropy decreases as energy increases, and high-energy states necessarily have negative Boltzmann temperature.
The limited range of states accessible to a system with negative temperature means that negative temperature is associated with emergent ordering of the system at high energies. For example in Onsager's point-vortex analysis negative temperature is associated with the emergence of large-scale clusters of vortices. This spontaneous ordering in equilibrium statistical mechanics goes against common physical intuition that increased energy leads to increased disorder.
It seems negative temperatures were first found experimentally in 1951, when Purcell and Pound observed evidence for them in the nuclear spins of a lithium fluoride crystal placed in a magnetic field, and then removed from this field. They wrote:
A system in a negative temperature state is not cold, but very hot, giving up energy to any system at positive temperature put into contact with it. It decays to a normal state through infinite temperature.
Definition of temperature
The absolute temperature (Kelvin) scale can be loosely interpreted as the average kinetic energy of the system's particles. The existence of negative temperature, let alone negative temperature representing "hotter" systems than positive temperature, would seem paradoxical in this interpretation. The paradox is resolved by considering the more rigorous definition of thermodynamic temperature in terms of Boltzmann's entropy formula. This reveals the tradeoff between internal energy and entropy contained in the system, with "coldness", the reciprocal of temperature, being the more fundamental quantity. Systems with a positive temperature will increase in entropy as one adds energy to the system, while systems with a negative temperature will decrease in entropy as one adds energy to the system.
The definition of thermodynamic temperature is a function of the change in the system's entropy under reversible heat transfer :
Entropy being a state function, the integral of over any cyclical process is zero. For a system in which the entropy is purely a function of the system's energy , the temperature can be defined as:
Equivalently, thermodynamic beta, or "coldness", is defined as
where is the Boltzmann constant.
Note that in classical thermodynamics, is defined in terms of temperature. This is reversed here, is the statistical entropy, a function of the possible microstates of the system, and temperature conveys information on the distribution of energy levels among the possible microstates. For systems with many degrees of freedom, the statistical and thermodynamic definitions of entropy are generally consistent with each other.
Some theorists have proposed using an alternative definition of entropy as a way to resolve perceived inconsistencies between statistical and thermodynamic entropy for small systems and systems where the number of states decreases with energy, and the temperatures derived from these entropies are different. It has been argued that the new definition would create other inconsistencies; its proponents have argued that this is only apparent.
Heat and molecular energy distribution
Negative temperatures can only exist in a system where there are a limited number of energy states (see below). As the temperature is increased on such a system, particles move into higher and higher energy states, so that the number of particles in the lower energy states and in the higher energy states approaches equality. (This is a consequence of the definition of temperature in statistical mechanics for systems with limited states.) By injecting energy into these systems in the right fashion, it is possible to create a system in which there are more particles in the higher energy states than in the lower ones. The system can then be characterized as having a negative temperature.
A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature. As Kittel and Kroemer (p. 462) put it,
The corresponding inverse temperature scale, for the quantity (where is the Boltzmann constant), runs continuously from low energy to high as +∞, …, 0, …, −∞. Because it avoids the abrupt jump from +∞ to −∞, is considered more natural than . Although a system can have multiple negative temperature regions and thus have −∞ to +∞ discontinuities.
In many familiar physical systems, temperature is associated to the kinetic energy of atoms. Since there is no upper bound on the momentum of an atom, there is no upper bound to the number of energy states available when more energy is added, and therefore no way to get to a negative temperature. However, in statistical mechanics, temperature can correspond to other degrees of freedom than just kinetic energy (see below).
Temperature and disorder
The distribution of energy among the various translational, vibrational, rotational, electronic, and nuclear modes of a system determines the macroscopic temperature. In a "normal" system, thermal energy is constantly being exchanged between the various modes.
However, in some situations, it is possible to isolate one or more of the modes. In practice, the isolated modes still exchange energy with the other modes, but the time scale of this exchange is much slower than for the exchanges within the isolated mode. One example is the case of nuclear spins in a strong external magnetic field. In this case, energy flows fairly rapidly among the spin states of interacting atoms, but energy transfer between the nuclear spins and other modes is relatively slow. Since the energy flow is predominantly within the spin system, it makes sense to think of a spin temperature that is distinct from the temperature associated to other modes.
A definition of temperature can be based on the relationship:
The relationship suggests that a positive temperature corresponds to the condition where entropy, , increases as thermal energy, , is added to the system. This is the "normal" condition in the macroscopic world, and is always the case for the translational, vibrational, rotational, and non-spin-related electronic and nuclear modes. The reason for this is that there are an infinite number of these types of modes, and adding more heat to the system increases the number of modes that are energetically accessible, and thus increases the entropy.
Examples
Noninteracting two-level particles
The simplest example, albeit a rather nonphysical one, is to consider a system of particles, each of which can take an energy of either or but are otherwise noninteracting. This can be understood as a limit of the Ising model in which the interaction term becomes negligible. The total energy of the system is
where is the sign of the th particle and is the number of particles with positive energy minus the number of particles with negative energy. From elementary combinatorics, the total number of microstates with this amount of energy is a binomial coefficient:
By the fundamental assumption of statistical mechanics, the entropy of this microcanonical ensemble is
We can solve for thermodynamic beta () by considering it as a central difference without taking the continuum limit:
hence the temperature
This entire proof assumes the microcanonical ensemble with energy fixed and temperature being the emergent property. In the canonical ensemble, the temperature is fixed and energy is the emergent property. This leads to ( refers to microstates):
Following the previous example, we choose a state with two levels and two particles. This leads to microstates , , , and .
The resulting values for , , and all increase with and never need to enter a negative temperature regime.
Nuclear spins
The previous example is approximately realized by a system of nuclear spins in an external magnetic field. This allows the experiment to be run as a variation of nuclear magnetic resonance spectroscopy. In the case of electronic and nuclear spin systems, there are only a finite number of modes available, often just two, corresponding to spin up and spin down. In the absence of a magnetic field, these spin states are degenerate, meaning that they correspond to the same energy. When an external magnetic field is applied, the energy levels are split, since those spin states that are aligned with the magnetic field will have a different energy from those that are anti-parallel to it.
In the absence of a magnetic field, such a two-spin system would have maximum entropy when half the atoms are in the spin-up state and half are in the spin-down state, and so one would expect to find the system with close to an equal distribution of spins. Upon application of a magnetic field, some of the atoms will tend to align so as to minimize the energy of the system, thus slightly more atoms should be in the lower-energy state (for the purposes of this example we will assume the spin-down state is the lower-energy state). It is possible to add energy to the spin system using radio frequency techniques. This causes atoms to flip from spin-down to spin-up.
Since we started with over half the atoms in the spin-down state, this initially drives the system towards a 50/50 mixture, so the entropy is increasing, corresponding to a positive temperature. However, at some point, more than half of the spins are in the spin-up position. In this case, adding additional energy reduces the entropy, since it moves the system further from a 50/50 mixture. This reduction in entropy with the addition of energy corresponds to a negative temperature. In NMR spectroscopy, this corresponds to pulses with a pulse width of over 180° (for a given spin). While relaxation is fast in solids, it can take several seconds in solutions and even longer in gases and in ultracold systems; several hours were reported for silver and rhodium at picokelvin temperatures. It is still important to understand that the temperature is negative only with respect to nuclear spins. Other degrees of freedom, such as molecular vibrational, electronic and electron spin levels are at a positive temperature, so the object still has positive sensible heat. Relaxation actually happens by exchange of energy between the nuclear spin states and other states (e.g. through the nuclear Overhauser effect with other spins).
Lasers
This phenomenon can also be observed in many lasing systems, wherein a large fraction of the system's atoms (for chemical and gas lasers) or electrons (in semiconductor lasers) are in excited states. This is referred to as a population inversion.
The Hamiltonian for a single mode of a luminescent radiation field at frequency is
The density operator in the grand canonical ensemble is
For the system to have a ground state, the trace to converge, and the density operator to be generally meaningful, must be positive semidefinite. So if , and is negative semidefinite, then must itself be negative, implying a negative temperature.
Motional degrees of freedom
Negative temperatures have also been achieved in motional degrees of freedom. Using an optical lattice, upper bounds were placed on the kinetic energy, interaction energy and potential energy of cold potassium-39 atoms. This was done by tuning the interactions of the atoms from repulsive to attractive using a Feshbach resonance and changing the overall harmonic potential from trapping to anti-trapping, thus transforming the Bose-Hubbard Hamiltonian from . Performing this transformation adiabatically while keeping the atoms in the Mott insulator regime, it is possible to go from a low entropy positive temperature state to a low entropy negative temperature state. In the negative temperature state, the atoms macroscopically occupy the maximum momentum state of the lattice. The negative temperature ensembles equilibrated and showed long lifetimes in an anti-trapping harmonic potential.
Two-dimensional vortex motion
The two-dimensional systems of vortices confined to a finite area can form thermal equilibrium states at negative temperature, and indeed negative temperature states were first predicted by Onsager in his analysis of classical point vortices. Onsager's prediction was confirmed experimentally for a system of quantum vortices in a Bose-Einstein condensate in 2019.
See also
Negative resistance
Two's complement
References
Further reading
External links
Temperature
Entropy
Magnetism
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362,779 | https://en.wikipedia.org/wiki/Swatch%20Internet%20Time | Swatch Internet Time (or ) is a decimal time system introduced in 1998 by the Swatch corporation as part of the marketing campaign for their line of ".beat" watches. Those without a watch could use the Internet to view the current time on the watchmaker's website, but now a dedicated wiki serves the purpose. The concept of .beat time is similar to decimal minutes in French Revolutionary decimal time.
Instead of hours and minutes, in Swatch Time the mean solar day is divided into 1,000 equal parts called s, meaning each lasts in standard time. The time of day always references the amount of time that has passed since midnight (standard time) in Biel, Switzerland, where Swatch's headquarters is located. For example, @248 BEATS indicates a time 248 after midnight, or of a day (just over 5 hours and 57 minutes; or 5:57 AM UTC+1).
There are no time zones in Swatch Internet Time; it is a globally unified timekeeping system based on what Swatch calls "Biel Mean Time" (BMT), the time zone conventionally known as Central European Time or West Africa Time. Note that it is based on the time zone and not the actual mean solar time measured in Biel. Also, unlike civil time in Switzerland and many other countries, Swatch Internet Time has never observed daylight saving time (DST), even prior to more recent decisions to abandon DST in certain locales.
History
Swatch Internet Time was announced on 23 October 1998, in a ceremony at the Junior Summit '98, attended by Nicolas G. Hayek, president and CEO of the Swatch Group, G.N. Hayek, president of Swatch Ltd., and Nicholas Negroponte, founder and then director of the MIT Media Lab. During the summit, Swatch Internet Time became the official time system for Nation.1, an online country (supposedly) created and run by children.
Uses
During 1999, Swatch produced several models of watch, branded "Swatch ", that displayed Swatch Internet Time as well as standard time, and even convinced a few websites (such as CNN.com) to use the new format. PHP's date() function has a format specifier, 'B', which returns the Swatch Internet Time notation for a given time stamp. It was also used as a time reference on ICQ, and the online role-playing game Phantasy Star Online used it since its launch on the Dreamcast in 2000 to try to facilitate cross-continent gaming (as the game allowed Japanese, American and European players to mingle on the same servers). In March 2001, Ericsson released the T20e, a mobile phone which gave the user the option of displaying Internet Time. Outside these areas, it is infrequently used. While Swatch still offers the concept on its website, it no longer markets Beat watches. In July 2016, Swatch released Touch Zero Two, its second wirelessly connected watch, with Swatch Internet Time function.
Beatnik satellite controversy
In early 1999, Swatch began a marketing campaign about the launch of their Beatnik satellite, intended to service a set of Internet Time watches. They were criticized for planning to use an amateur radio frequency for broadcasting a commercial message (an act banned by international treaties). The satellite was intended to be deployed by hand from the Mir space station. Swatch instead donated the transmitter batteries for use in normal Mir functions, and the satellite never broadcast.
Description
The concept was touted as an alternative, decimal measure of time. One of the supposed goals was to simplify the way people in different time zones communicate about time, mostly by eliminating time zones altogether. It also does away with the division of the day into 12 or 24 parts (hours), then 60 parts (minutes), then 60 parts (seconds), then 1000 parts (milliseconds). Furthermore, there is no confusion between the AM/PM system and 24-hour time.
Beats
Instead of hours and minutes, the mean solar day is divided into 1,000 parts called . Each lasts 1 minute and 26.4 seconds. One is equal to one decimal minute in French decimal time.
Although Swatch does not specify units smaller than one , third party implementations have extended the standard by adding "centibeats" or "sub-beats", for extended precision: @248.00. Each "centibeat" is a hundredth of a and is therefore equal to one French decimal second (0.864 seconds).
Time zones
There are no time zones; instead, the new time scale of Biel Mean Time (BMT) is used, based on the company's headquarters in Biel, Switzerland. Despite the name, BMT does not refer to mean solar time at the Biel meridian (7°15′E), but to the standard time there. It is equivalent to Central European Time and West Africa Time, or UTC+1.
Like UTC, Swatch Internet Time is the same throughout the world. For example, when the time is 875 , or @875, in New York, it is also @875 in Tokyo. Unlike civil time in most European countries, Internet Time does not observe daylight saving time, and thus it matches Central European Time during (European) winter and Western European Summer Time, which is observed by the United Kingdom, Ireland, Portugal and Spain's Canary Islands during summer.
Notation
The most distinctive aspect of Swatch Internet Time is its notation; as an example, "@248" would indicate a time 248 after midnight, equivalent to a fractional day of 0.248 CET, or 04:57:07.2 UTC. No explicit format was provided for dates, although the Swatch website formerly displayed the Gregorian calendar date in the order day-month-year, separated by periods and prefixed by the letter d (e.g. d31.01.99).
Calculation from UTC+1
The formula for calculating the time in from UTC+1 is:
Where h is UTC+1 hours and m is UTC+1 minutes. The result is rounded down.
When does the day begin?
Example cities across the globe @000 BEATS midnight:
See also
Traditional Chinese timekeeping – 1 = 10 'beats'
Metric time
New Earth Time
Unix time
Notes
References
External links
A short description of Internet time
Swatch Internet Time
Time measurement systems
Internet properties established in 1998
Units of time
Decimal time
Swiss inventions
1998 in Switzerland | Swatch Internet Time | [
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362,828 | https://en.wikipedia.org/wiki/Bruno%20Latour | Bruno Latour (; 22 June 1947 – 9 October 2022) was a French philosopher, anthropologist and sociologist. He was especially known for his work in the field of science and technology studies (STS). After teaching at the École des Mines de Paris (Centre de Sociologie de l'Innovation) from 1982 to 2006, he became professor at Sciences Po Paris (2006–2017), where he was the scientific director of the Sciences Po Medialab. He retired from several university activities in 2017. He was also a Centennial Professor at the London School of Economics.
Latour is best known for his books We Have Never Been Modern (1991; English translation, 1993), Laboratory Life (with Steve Woolgar, 1979) and Science in Action (1987). Although his studies of scientific practice were at one time associated with social constructionist approaches to the philosophy of science, Latour diverged significantly from such approaches. He was best known for withdrawing from the subjective/objective division and re-developing the approach to work in practice. Latour said in 2017 that he is interested in helping to rebuild trust in science and that some of the authority of science needs to be regained.
Along with Michel Callon, Madeleine Akrich, and John Law, Latour is one of the primary developers of actor–network theory (ANT), a constructionist approach influenced by the ethnomethodology of Harold Garfinkel, the generative semiotics of Algirdas Julien Greimas, and (more recently) the sociology of Émile Durkheim's rival Gabriel Tarde.
Biography
Latour was related to a well-known family of winemakers from Burgundy known as Maison Louis Latour, but was not associated with the similarly named Château Latour estate in Bordeaux.
As a student, Latour originally focused on philosophy. In 1971–1972, he ranked second and then first (reçu second, premier) in the French national competitive exam /CAPES de philosophies. Latour went on to earn his PhD degree in philosophical theology at the University of Tours in 1975. His thesis title was Exégèse et ontologie: une analyse des textes de resurrection (Exegesis and Ontology: An Analysis of the Texts of Resurrection).
Latour developed an interest in anthropology, and undertook fieldwork in Ivory Coast, on behalf of ORSTOM, which resulted in a brief monograph on decolonization, race, and industrial relations. In the 1990s, he engaged in a series of dialogues with Michel Serres that were published as Eclaircissements (Conversations on Science, Culture and Time).
After spending more than twenty years (1982–2006) at the Centre de sociologie de l'innovation at the École des Mines in Paris, Latour moved in 2006 to Sciences Po, where he was the first occupant of a chair named for Gabriel Tarde. In recent years he also served as one of the curators of successful art exhibitions at the Zentrum für Kunst und Medientechnologie in Karlsruhe, Germany, including "Iconoclash" (2002) and "Making Things Public" (2005). In 2005, he also held the Spinoza Chair of Philosophy at the University of Amsterdam.
Latour remained religious until the end of his life, reading the Bible "devotedly."
Latour died from pancreatic cancer on 9 October 2022, at the age of 75. His papers were contributed to the French National Archives and the Municipal Archives of Beaune.
Awards and honors
On 22 May 2008, Latour was awarded an honorary doctorate by the Université de Montréal on the occasion of an organizational communication conference held in honor of the work of James R. Taylor, on whom Latour has had an important influence. He held several other honorary doctorates, as well as France's Légion d'Honneur (2012).
Holberg Prize
On 13 March 2013, he was announced as the winner of the 2013 Holberg Prize. The prize committee stated that "Bruno Latour has undertaken an ambitious analysis and reinterpretation of modernity, and has challenged fundamental concepts such as the distinction between modern and pre-modern, nature and society, human and non-human." The committee states that "the impact of Latour's work is evident internationally and far beyond studies of the history of science, art history, history, philosophy, anthropology, geography, theology, literature and law."
A 2013 article in Aftenposten by Norwegian philosopher Jon Elster criticised the conferment to Latour, by saying "The question is, does he deserve the prize. ... If the statutes [of the award] had used new knowledge as the main criteria, instead as one of several, then he would be completely unqualified in my opinion."
Spinoza and Kyoto Prize
The Dutch "International Spinozaprijs Foundation" awarded the "Spinozalens 2020" to Bruno Latour on 24 November 2020.
In 2021 he received the Kyoto Prize in the category "Thought and Ethics".
Main works
Laboratory Life
After his early career efforts, Latour shifted his research interests to focus on laboratory scientists. Latour rose in importance following the 1979 publication of Laboratory Life: the Social Construction of Scientific Facts with co-author Steve Woolgar. In the book, the authors undertake an ethnographic study of a neuroendocrinology research laboratory at the Salk Institute. This early work argued that naïve descriptions of the scientific method, in which theories stand or fall on the outcome of a single experiment, are inconsistent with actual laboratory practice.
In the laboratory, Latour and Woolgar observed that a typical experiment produces only inconclusive data that is attributed to failure of the apparatus or experimental method, and that a large part of scientific training involves learning how to make the subjective decision of what data to keep and what data to throw out. Latour and Woolgar argued that, for untrained observers, the entire process resembles not an unbiased search for truth and accuracy but a mechanism for ignoring data that contradicts scientific orthodoxy.
Latour and Woolgar produced a highly heterodox and controversial picture of the sciences. Drawing on the work of Gaston Bachelard, they advance the notion that the objects of scientific study are socially constructed within the laboratory—that they cannot be attributed with an existence outside of the instruments that measure them and the minds that interpret them. They view scientific activity as a system of beliefs, oral traditions and culturally specific practices—in short, science is reconstructed not as a procedure or as a set of principles but as a culture. Latour's 1987 book Science in Action: How to Follow Scientists and Engineers through Society is one of the key texts of the sociology of scientific knowledge in which he famously wrote his Second Principle as follows: "Scientist and engineers speak in the name of new allies that they have shaped and enrolled; representatives among other representatives, they add these unexpected resources to tip the balance of force in their favor."
Some of Latour's position and findings in this era provoked vehement rebuttals. Gross and Leavitt argue that Latour's position becomes absurd when applied to non-scientific contexts: e.g., if a group of coworkers in a windowless room were debating whether or not it were raining outside and went outdoors to discover raindrops in the air and puddles on the soil, Latour's hypothesis would assert that the rain was socially constructed. Similarly, philosopher John Searle argues that Latour's "extreme social constructivist" position is seriously flawed on several points, and furthermore has inadvertently "comical results".
The Pasteurization of France
After a research project examining the sociology of primatologists, Latour followed up the themes in Laboratory Life with Les Microbes: guerre et paix (published in English as The Pasteurization of France in 1988). In it, he reviews the life and career of one of France's most famous scientists Louis Pasteur and his discovery of microbes, in the fashion of a political biography. Latour highlights the social forces at work in and around Pasteur's career and the uneven manner in which his theories were accepted. By providing more explicitly ideological explanations for the acceptance of Pasteur's work more easily in some quarters than in others, he seeks to undermine the notion that the acceptance and rejection of scientific theories is primarily, or even usually, a matter of experiment, evidence or reason.
Aramis, or The Love of Technology
Aramis, or The Love of Technology focuses on the history of an unsuccessful mass-transit project. Aramis PRT (personal rapid transit), a high tech automated subway, had been developed in France during the 70s and 80s and was supposed to be implemented as a personal rapid transit system in Paris. It combined the flexibility of an automobile with the efficiency of a subway. Aramis was to be an ideal urban transportation system based on private cars in constant motion and the elimination of unnecessary transfers. This new form of transportation was intended to be as secure and inexpensive as collective transportation. The proposed system had custom-designed motors, sensors, controls, digital electronics, software and a major installation in southern Paris. But in the end the project died in 1987. Latour argues that the technology failed not because any particular actor killed it, but because the actors failed to sustain it through negotiation and adaptation to a changing social situation. While investigating Aramis's demise, Latour delineates the tenets of actor-network theory. According to Latour's own description of the book, the work aims "at training readers in the booming field of technology studies and at experimenting in the many new literary forms that are necessary to handle mechanisms and automatisms without using the belief that they are mechanical or automatic."
We Have Never Been Modern
Latour's work Nous n'avons jamais été modernes : Essai d'anthropologie symétrique was first published in French in 1991, and then in English in 1993 as We Have Never Been Modern.
Latour encouraged the reader of this anthropology of science to re-think and re-evaluate our mental landscape. He evaluated the work of scientists and contemplated the contribution of the scientific method to knowledge and work, blurring the distinction across various fields and disciplines.
Latour argued that society has never really been modern and promoted nonmodernism (or amodernism) over postmodernism, modernism, or antimodernism. His stance was that we have never been modern and minor divisions alone separate Westerners now from other collectives. Latour viewed modernism as an era that believed it had annulled the entire past in its wake. He presented the antimodern reaction as defending such entities as spirit, rationality, liberty, society, God, or even the past. Postmoderns, according to Latour, also accepted the modernistic abstractions as if they were real. In contrast, the nonmodern approach reestablished symmetry between science and technology on the one hand and society on the other. Latour also referred to the impossibility of returning to premodernism because it precluded the large scale experimentation which was a benefit of modernism.
Latour attempted to prove through case studies the fallacy in the old object/subject and Nature/Society compacts of modernity, which can be traced back to Plato. He refused the concept of "out there" versus "in here". He rendered the object/subject distinction as simply unusable and charted a new approach towards knowledge, work, and circulating reference. Latour considered nonmoderns to be playing on a different field, one vastly different to that of post-moderns. He referred to it as much broader and much less polemical, a creation of an unknown territory, which he playfully referred to as the Middle Kingdom.
In 1998, historian of science Margaret C. Jacob argued that Latour's politicized account of the development of modernism in the 17th century is "a fanciful escape from modern Western history".
Pandora's Hope
Pandora's Hope (1999) marks a return to the themes Latour explored in Science in Action and We Have Never Been Modern. It uses independent but thematically linked essays and case studies to question the authority and reliability of scientific knowledge. Latour uses a narrative, anecdotal approach in a number of the essays, describing his work with pedologists in the Amazon rainforest, the development of the pasteurization process, and the research of French atomic scientists at the outbreak of the Second World War. Latour states that this specific, anecdotal approach to science studies is essential to gaining a full understanding of the discipline: "The only way to understand the reality of science studies is to follow what science studies do best, that is, paying close attention to the details of scientific practice" (p. 24). Some authors have criticized Latour's methodology, including Katherine Pandora, a history of science professor at the University of Oklahoma. In her review of Pandora's Hope, Katherine Pandora states:
"[Latour's] writing can be stimulating, fresh and at times genuinely moving, but it can also display a distractingly mannered style in which a rococo zeal for compounding metaphors, examples, definitions and abstractions can frustrate even readers who approach his work with the best of intentions (notwithstanding the inclusion of a nine-page glossary of terms and liberal use of diagrams in an attempt to achieve the utmost clarity)".
In addition to his epistemological concerns, Latour also explores the political dimension of science studies in Pandora's Hope. Two of the chapters draw on Plato's Gorgias as a means of investigating and highlighting the distinction between content and context. As Katherine Pandora states in her review:
"It is hard not to be caught up in the author's obvious delight in deploying a classic work from antiquity to bring current concerns into sharper focus, following along as he manages to leave the reader with the impression that the protagonists Socrates and Callicles are not only in dialogue with each other but with Latour as well."
Although Latour frames his discussion with a classical model, his examples of fraught political issues are all current and of continuing relevance: global warming, the spread of mad cow disease, and the carcinogenic effects of smoking are all mentioned at various points in Pandora's Hope. In Felix Stalder's article "Beyond constructivism: towards a realistic realism", he summarizes Latour's position on the political dimension of science studies as follows: "These scientific debates have been artificially kept open in order to render impossible any political action against these problems and those who profit from them".
"Why Has Critique Run Out of Steam?"
In a 2004 article, Latour questioned the fundamental premises on which he had based most of his career, asking, "Was I wrong to participate in the invention of this field known as science studies?" He undertakes a trenchant critique of his own field of study and, more generally, of social criticism in contemporary academia. He suggests that critique, as currently practiced, is bordering on irrelevancy. To maintain any vitality, Latour argues that social critiques require a drastic reappraisal: "our critical equipment deserves as much critical scrutiny as the Pentagon budget." (p. 231) To regain focus and credibility, Latour argues that social critiques must embrace empiricism, to insist on the "cultivation of a stubbornly realist attitude – to speak like William James". (p. 233)
Latour suggests that about 90 per cent of contemporary social criticism displays one of two approaches which he terms "the fact position and the fairy position." (p. 237) The fairy position is anti-fetishist, arguing that "objects of belief" (e.g., religion, arts) are merely concepts created by the projected wishes and desires of the "naive believer"; the "fact position" argues that individuals are dominated, often covertly and without their awareness, by external forces (e.g., economics, gender). (p. 238) "Do you see now why it feels so good to be a critical mind?" asks Latour: no matter which position you take, "You're always right!" (p. 238–239) Social critics tend to use anti-fetishism against ideas they personally reject; to use "an unrepentant positivist" approach for fields of study they consider valuable; all the while thinking as "a perfectly healthy sturdy realist for what you really cherish." (p. 241) These inconsistencies and double standards go largely unrecognized in social critique because "there is never any crossover between the two lists of objects in the fact position and the fairy position." (p. 241)
The practical result of these approaches being taught to millions of students in elite universities for several decades is a widespread and influential "critical barbarity" that has—like a malign virus created by a "mad scientist"—thus far proven impossible to control. Most troubling, Latour notes that critical ideas have been appropriated by those he describes as conspiracy theorists, including global warming deniers and the 9/11 Truth movement: "Maybe I am taking conspiracy theories too seriously, but I am worried to detect, in those mad mixtures of knee-jerk disbelief, punctilious demands for proofs, and free use of powerful explanation from the social neverland, many of the weapons of social critique." (p. 230)
The conclusion of the article is to argue for a positive framing of critique, to help understand how matters of concern can be supported rather than undermined: "The critic is not the one who lifts the rugs from under the feet of the naïve believers, but the one who offers the participants arenas in which to gather. The critic is not the one who alternates haphazardly between antifetishism and positivism like the drunk iconoclast drawn by Goya, but the one for whom, if something is constructed, then it means it is fragile and thus in great need of care and caution."
Latour's article has been highly influential within the field of postcritique, an intellectual movement within literary criticism and cultural studies that seeks to find new forms of reading and interpretation that go beyond the methods of critique, critical theory, and ideological criticism. The literary critic Rita Felski has named Latour as an important precursor to the project of postcritique.
Reassembling the Social
In Reassembling the Social (2005), Latour continues a reappraisal of his work, developing what he calls a "practical metaphysics", which calls "real" anything that an actor (one whom we are studying) claims as a source of motivation for action. So if someone says, "I was inspired by God to be charitable to my neighbors" we are obliged to recognize the "ontological weight" of their claim, rather than attempting to replace their belief in God's presence with "social stuff", like class, gender, imperialism, etc. Latour's nuanced metaphysics demands the existence of a plurality of worlds, and the willingness of the researcher to chart ever more. He argues that researchers must give up the hope of fitting their actors into a structure or framework, but Latour believes the benefits of this sacrifice far outweigh the downsides: "Their complex metaphysics would at least be respected, their recalcitrance recognized, their objections deployed, their multiplicity accepted."
For Latour, to talk about metaphysics or ontology—what really is—means paying close empirical attention to the various, contradictory institutions and ideas that bring people together and inspire them to act. Here is Latour's description of metaphysics:
If we call metaphysics the discipline inspired by the philosophical tradition that purports to define the basic structure of the world, then empirical metaphysics is what the controversies over agencies lead to since they ceaselessly populate the world with new drives and, as ceaselessly, contest the existence of others. The question then becomes how to explore the actors' own metaphysics.
A more traditional metaphysicist might object, arguing that this means there are multiple, contradictory realities, since there are "controversies over agencies" – since there is a plurality of contradictory ideas that people claim as a basis for action (God, nature, the state, sexual drives, personal ambition, and so on). This objection manifests the most important difference between traditional philosophical metaphysics and Latour's nuance: for Latour, there is no "basic structure of reality" or a single, self-consistent world. An unknowably large multiplicity of realities, or "worlds" in his terms, exists–one for each actor's sources of agency, inspirations for action. In this Latour is remarkably close to B.F. Skinner's position in Beyond Freedom and Dignity and the philosophy of Radical Behaviorism. Actors bring "the real" (metaphysics) into being. The task of the researcher is not to find one "basic structure" that explains agency, but to recognize "the metaphysical innovations proposed by ordinary actors". Mapping those metaphysical innovations involves a strong dedication to relativism, Latour argues. The relativist researcher "learns the actors' language," records what they say about what they do, and does not appeal to a higher "structure" to "explain" the actor's motivations. The relativist "takes seriously what [actors] are obstinately saying" and "follows the direction indicated by their fingers when they designate what 'makes them act'". The relativist recognizes the plurality of metaphysics that actors bring into being, and attempts to map them rather than reducing them to a single structure or explanation.
In the science wars
Alan Sokal, in his Fashionable Nonsense, criticized Latour's relativism by referring to an article written by Latour in La Recherche in 1998. In his reaction to research showing that the pharaoh Ramses II probably died of tuberculosis, Latour thought "How could he pass away due to a bacillus discovered by Koch in 1882? ... Before Koch, the bacillus has no real existence." He says that it is as much of an anachronism as it would be to claim that the pharaoh died of machine-gun fire.
Latour noted that he had been asked "Do you believe in reality?", which caused a "quick and laughing answer". Reality, for Latour, is neither something we have to believe in nor do we have lost access to it in the first place. "'Do you believe in reality?' To ask such a question one has to become so distant from reality that the fear of losing it entirely becomes plausible—and this fear itself has an intellectual history [...] Only a mind put in the strangest position, looking at a world from inside out and linked to the outside by nothing but the tenuous connection of the gaze, will throb in the constant fear of losing reality; only such a bodiless observer will desperately look for some absolute life-supporting survival kit."According to Latour, the originality of science studies lies in demonstrating that facts are both real and constructed. The accusation of a postmodern hostility to science, thus, not only fails to recognize that science studies aims at a more robust understanding how science is done in practice, but also shows a fundamental misunderstanding of the methods and insights of science studies. In fact, Latour has emphatically problematized the rise of anti-scientific thinking and so-called "alternative facts" For Latour, the recent attacks against climate sciences and other disciplines demonstrate that there is a real war on science going on requiring a more intimate cooperation between science and science studies.
Selected bibliography
Books
Originally published 1979 in Los Angeles, by SAGE Publications
Latour, Bruno (2024). How to Inhabit the Earth. Interviews with Nicolas Truong. Translated by Julie Rose. Cambridge, UK: Polity Press. ISBN 978-1-5095-5946-6.
Chapters in books
Journal articles
See also
New materialisms
Social construction of technology
Technological determinism
References
Sources
External links
Bruno Latour's website
1947 births
2022 deaths
People from Beaune
Sociologists of science
Science and technology studies scholars
Social constructionism
Materialists
Sociology of scientific knowledge
French sociologists
21st-century French anthropologists
Academic staff of Mines Paris - PSL
Actor-network theory
French Roman Catholics
Catholic philosophers
Holberg Prize laureates
French male writers
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21st-century French philosophers
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Recipients of the Legion of Honour
20th-century male writers
21st-century male writers
Academic staff of Sciences Po
Deaths from pancreatic cancer in France
Kyoto laureates in Arts and Philosophy
20th-century French anthropologists | Bruno Latour | [
"Physics",
"Technology"
] | 5,153 | [
"Materialists",
"Actor-network theory",
"Science and technology studies",
"Science and technology studies scholars",
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362,895 | https://en.wikipedia.org/wiki/Caryatid | A caryatid ( ; ; ) is a sculpted female figure serving as an architectural support taking the place of a column or a pillar supporting an entablature on her head. The Greek term karyatides literally means "maidens of Karyai", an ancient town on the Peloponnese. Karyai had a temple dedicated to the goddess Artemis in her aspect of Artemis Karyatis: "As Karyatis she rejoiced in the dances of the nut-tree village of Karyai, those Karyatides, who in their ecstatic round-dance carried on their heads baskets of live reeds, as if they were dancing plants".
An atlas or atlantid or telamon is a male version of a caryatid, i.e., a sculpted male statue serving as an architectural support.
Etymology
The term is first recorded in the Latin form caryatides by the Roman architect Vitruvius. He stated in his 1st century BC work De architectura (I.1.5) that certain female figures represented the punishment of the women of Caryae, a town near Sparta in Laconia, who were condemned to slavery after betraying Athens by siding with Persia in the Greco-Persian Wars. However, Vitruvius's explanation is doubtful; well before the Persian Wars, female figures were used as decorative supports in Greece and the ancient Near East. Vitruvius's explanation is dismissed as an error by Camille Paglia in Glittering Images and not even mentioned by Mary Lefkowitz in Black Athena Revisited. They both say the term refers to young women worshipping Artemis in Caryae through dance. Lefkowitz says that the term comes from the Spartan city of Caryae, where young women did a ring dance around an open-air statue of the goddess Artemis, locally identified with a walnut tree. Bernard Sergent specifies that the dancers came to the small town of Caryae from nearby Sparta. Nevertheless, the association of caryatids with slavery persists and is prevalent in Renaissance art.
The ancient Caryae supposedly was one of the six adjacent villages that united to form the original township of Sparta, and the hometown of Menelaos' queen, Helen of Troy. Girls from Caryae were considered especially beautiful, strong, and capable of giving birth to strong children.
A caryatid supporting a basket on her head is called a canephora ("basket-bearer"), representing one of the maidens who carried sacred objects used at feasts of the goddesses Athena and Artemis. The Erectheion caryatids, in a shrine dedicated to an archaic king of Athens, may therefore represent priestesses of Artemis in Caryae, a place named for the "nut-tree sisterhood" – apparently in Mycenaean times, like other plural feminine toponyms, such as Hyrai or Athens itself.
The later male counterpart of the caryatid is referred to as a telamon (plural telamones) or atlas (plural atlantes) – the name refers to the legend of Atlas, who bore the sphere of the heavens on his shoulders. Such figures were used on a monumental scale, notably in the Temple of Olympian Zeus in Agrigento, Sicily.
Ancient usage
Some of the earliest known examples were found in the treasuries of Delphi, including that of Siphnos, dating to the 6th century BC. However, their use as supports in the form of women can be traced back even earlier, to ritual basins, ivory mirror handles from Phoenicia, and draped figures from archaic Greece.
The best-known and most-copied examples are those of the six figures of the Caryatid porch of the Erechtheion on the Acropolis at Athens. One of those original six figures, removed by Lord Elgin in the early 19th century in an act which severely damaged the temple and is widely considered to be vandalism and looting, is currently in the British Museum in London. The Greek government does not recognise the British Museum's claims to own any part of the Acropolis temples and the return of the stolen Caryatid to Athens along with the rest of the so-called Elgin Marbles is the subject of a major international campaign. The Acropolis Museum holds the other five figures, which are replaced onsite by replicas. The five originals that are in Athens are now being exhibited in the new Acropolis Museum, on a special balcony that allows visitors to view them from all sides. The pedestal for the caryatid removed to London remains empty, awaiting its return. From 2011 to 2015, they were cleaned by a specially constructed laser beam, which removed accumulated soot and grime without harming the marble's patina. Each caryatid was cleaned in place, with a television circuit relaying the spectacle live to museum visitors.
Although of the same height and build, and similarly attired and coiffed, the six Caryatids are not the same: their faces, stance, draping, and hair are carved separately; the three on the left stand on their right foot, while the three on the right stand on their left foot. Their bulky, intricately arranged hairstyles serve the crucial purpose of providing static support to their necks, which would otherwise be the thinnest and structurally weakest part.
The Romans also copied the Erechtheion caryatids, installing copies in the Forum of Augustus and the Pantheon in Rome, and at Hadrian's Villa at Tivoli. Another Roman example, found on the Via Appia, is the Townley Caryatid.
Renaissance and after
In Early Modern times, the practice of integrating caryatids into building facades was revived, and in interiors they began to be employed in fireplaces, which had not been a feature of buildings in Antiquity and offered no precedents. Early interior examples are the figures of Heracles and Iole carved on the jambs of a monumental fireplace in the Sala della Jole of the Doge's Palace, Venice, about 1450. In the following century Jacopo Sansovino, both sculptor and architect, carved a pair of female figures supporting the shelf of a marble chimneypiece at Villa Garzoni, near Padua. No architect mentioned the device until 1615, when Palladio's pupil Vincenzo Scamozzi included a chapter devoted to chimneypieces in his Idea della archittura universale. Those in the apartments of princes and important personages, he considered, might be grand enough for chimneypieces with caryatid supporters, such as one he illustrated and a similar one he installed in the Sala dell'Anticollegio, also in the Doge's Palace.
In the 16th century, from the examples engraved for Sebastiano Serlio's treatise on architecture, caryatids became a fixture in the decorative vocabulary of Northern Mannerism expressed by the Fontainebleau School and the engravers of designs in Antwerp. In the early 17th century, interior examples appear in Jacobean interiors in England; in Scotland the overmantel in the great hall of Muchalls Castle remains an early example. Caryatids remained part of the German Baroque vocabulary and were refashioned in more restrained and "Grecian" forms by neoclassical architects and designers, such as the four terracotta caryatids on the porch of St Pancras New Church, London (1822).
Many caryatids lined up on the facade of the 1893 Palace of the Arts housing the Museum of Science and Industry in Chicago. In the arts of design, the draped figure supporting an acanthus-grown basket capital taking the form of a candlestick or a table-support is a familiar cliché of neoclassical decorative arts. The John and Mable Ringling Museum of Art in Sarasota has caryatids as a motif on its eastern facade.
In 1905 American sculptor Augustus Saint Gaudens created a caryatid porch for the Albright–Knox Art Gallery in Buffalo, New York in which four of the eight figures (the other four figures holding only wreaths) represented a different art form, Architecture, Painting, Sculpture, and Music.
Auguste Rodin's 1881 sculpture Fallen Caryatid Carrying her Stone (part of his monumental The Gates of Hell work) shows a fallen caryatid. Robert Heinlein described this piece in Stranger in a Strange Land: "Now here we have another emotional symbol... for almost three thousand years or longer, architects have designed buildings with columns shaped as female figures... After all those centuries it took Rodin to see that this was work too heavy for a girl... Here is this poor little caryatid who has tried—and failed, fallen under the load.... She didn't give up, Ben; she's still trying to lift that stone after it has crushed her..."
In Act 2 of his 1953 play 'Waiting for Godot', author Samuel Beckett has Estragon say "We are not caryatids!" when he and Vladimir tire of "cart(ing) around" the recently blinded Pozzo.
Agnes Varda made two short films documenting Caryatid columns around Paris.
1984 Les Dites Cariatides
2005 Les Dites Cariatides Bis.
The musical group Son Volt evoke the caryatides and their burden borne in poetic metaphor on the song "Caryatid Easy" from their 1997 album Straightaways, with singer Jay Farrar reproving an unidentified lover with the line "you play the caryatid easy."
Gallery
See also
Caryatid stools in African art
Term (architecture)
The Sphere: Große Kugelkaryatide (Great Spherical Caryatid) – WTC sculpture by Fritz Koenig
A Greek Tragedy, 1987 Oscar-winning animated short about three caryatid statues.
References
External links
Kerényi, Karl (1951) 1980. The Gods of the Greeks (Thames & Hudson)
Conserving the Caryatids in the Acropolis Museum
Images of Caryatids of Athens (Spanish)
Acropolis of Athens
Ancient Greek architecture
Culture of ancient Greece
Columns and entablature
Architectural sculpture
Sculptures of women in Greece | Caryatid | [
"Technology"
] | 2,100 | [
"Structural system",
"Columns and entablature"
] |
362,930 | https://en.wikipedia.org/wiki/Diacetyl | Diacetyl ( ; IUPAC systematic name: butanedione or butane-2,3-dione) is an organic compound with the chemical formula (CH3CO)2. It is a yellow liquid with an intensely buttery flavor. It is a vicinal diketone (two C=O groups, side-by-side). Diacetyl occurs naturally in alcoholic beverages and some cheeses and is added as a flavoring to some foods to impart its buttery flavor. Chronic inhalation exposure to diacetyl fumes is a causative agent of the lung disease bronchiolitis obliterans, commonly known as "popcorn lung".
Chemical structure
A distinctive feature of diacetyl (and other vicinal diketones) is the long C–C bond linking the carbonyl centers. This bond distance is about 1.54 Å, compared to 1.45 Å for the corresponding C–C bond in 1,3-butadiene. The elongation is attributed to repulsion between the polarized carbonyl carbon centers.
Occurrence and biosynthesis
Diacetyl arises naturally as a byproduct of fermentation. In some fermentative bacteria, it is formed via the thiamine pyrophosphate-mediated condensation of pyruvate and acetyl CoA. Sour (cultured) cream, cultured buttermilk, and cultured butter are produced by inoculating pasteurized cream or milk with a lactic starter culture, churning (agitating) and holding the milk until a desired pH drop (or increase in acidity) is attained. Cultured cream, cultured butter, and cultured buttermilk owe their tart flavour to lactic acid bacteria and their buttery aroma and taste to diacetyl. Malic acid can be converted to lactic acid to make diacetyl.
Production
Diacetyl is produced industrially by dehydrogenation of 2,3-butanediol. Acetoin is an intermediate.
Applications
In food products
Diacetyl and acetoin are two compounds that give butter its characteristic taste. Because of this, manufacturers of artificial butter flavoring, margarines or similar oil-based products typically add diacetyl and acetoin (along with beta-carotene for the yellow color) to make the final product butter-flavored, because it would otherwise be relatively tasteless.
Electronic cigarettes
Diacetyl is used as a flavoring agent in some liquids used in electronic cigarettes. People nearby may be exposed to it in the exhaled aerosol at levels near the limit set for occupational exposure.
In alcoholic beverages
In some styles of beer (e.g. in many beer styles produced in the United Kingdom, such as stouts, English bitters, and Scottish ales), the presence of diacetyl can be acceptable or desirable at low or, in some cases, moderate levels. In other styles, its presence is considered a flaw or undesirable.
Diacetyl is produced during fermentation as a byproduct of valine synthesis, when yeast produces α-acetolactate, which escapes the cell and is spontaneously decarboxylated into diacetyl. The yeast then absorbs the diacetyl, and reduces the ketone groups to form acetoin and 2,3-butanediol.
Beer sometimes undergoes a "diacetyl rest", in which its temperature is raised slightly for two or three days after fermentation is complete, to allow the yeast to absorb the diacetyl it produced earlier in the fermentation cycle. The makers of some wines, such as chardonnay, deliberately promote the production of diacetyl because of the feel and flavor it imparts. Diacetyl is present in some chardonnays known as "butter bombs", although there is a trend back toward the more traditional French styles.
Concentrations from 0.005 mg/L to 1.7 mg/L were measured in chardonnay wines, and the amount needed for the flavor to be noticed is at least 0.2 mg/L.
Use as butter flavoring
Butter-flavoring controversy
Chronic industrial exposure to diacetyl fumes, such as in the microwave popcorn production industry, has been associated with bronchiolitis obliterans, a rare and life-threatening form of non-reversible obstructive lung disease in which the bronchioles (small airway branches) are compressed and narrowed by fibrosis (scar tissue) and/or inflammation.
Regulation
The European Commission has declared diacetyl is legal for use as a flavouring substance in all EU states. As a diketone, diacetyl is included in the EU's flavouring classification Flavouring Group Evaluation 11 (FGE.11). A Scientific Panel of the EU Commission evaluated six flavouring substances (not including diacetyl) from FGE.11 in 2004. As part of this study, the panel reviewed available studies on several other flavourings in FGE.11, including diacetyl. Based on the available data, the panel reiterated the finding that there were no safety concerns for diacetyl's use as a flavouring.
In 2007, the European Food Safety Authority (EFSA), the EU's food safety regulatory body, stated its scientific panel on food additives and flavourings (AFC) was evaluating diacetyl along with other flavourings as part of a larger study.
In 2007, the Flavor and Extract Manufacturers Association recommended reducing diacetyl in butter flavorings. Manufacturers of butter flavored popcorn including Pop Weaver, Trail's End, and ConAgra Foods (maker of Orville Redenbacher's and Act II) began removing diacetyl as an ingredient from their products.
A 2010 U.S. OSHA Safety and Health Information Bulletin and companion Worker Alert recommend employers use safety measures to minimize exposure to diacetyl or its substitutes.
In 2016, diacetyl was banned in e-liquids/e-cigarettes in the EU under the EU Tobacco Products Directive.
See also
Acetylpropionyl, a similar diketone
Acetoin
Bronchiolitis obliterans
References
Further reading
External links
Toxicology data
NIOSH Alert: Preventing Lung Disease and Workers who Use or Make Flavorings
A Case of Regulatory Failure – Popcorn Workers Lung, from www.defendingscience.org.
Scientists Urge Secretary of Labor to Protect Workers from Diacetyl, a press release from defendingscience.org. Links to studies on the health effects of diacetyl, and to a variety of related documents including the recent OSHA petition and the scientists' letter of support may be found here.
Flavoring suspected in illness, Washington Post, May 7, 2007.
NIOSH International Safety Card for 2,3-butanedione
National Institute for Occupational Safety and Health – Flavorings-Related Lung Disease
IFIC – Diacetyl
Diketones
Flavors
Popcorn
Chemical hazards
Conjugated ketones | Diacetyl | [
"Chemistry"
] | 1,487 | [
"Chemical hazards"
] |
362,983 | https://en.wikipedia.org/wiki/Many-one%20reduction | In computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances of one decision problem (whether an instance is in ) to another decision problem (whether an instance is in ) using a computable function. The reduced instance is in the language if and only if the initial instance is in its language . Thus if we can decide whether instances are in the language , we can decide whether instances are in its language by applying the reduction and solving for . Thus, reductions can be used to measure the relative computational difficulty of two problems. It is said that reduces to if, in layman's terms is at least as hard to solve as . This means that any algorithm that solves can also be used as part of a (otherwise relatively simple) program that solves .
Many-one reductions are a special case and stronger form of Turing reductions. With many-one reductions, the oracle (that is, our solution for ) can be invoked only once at the end, and the answer cannot be modified. This means that if we want to show that problem can be reduced to problem , we can use our solution for only once in our solution for , unlike in Turing reductions, where we can use our solution for as many times as needed in order to solve the membership problem for the given instance of .
Many-one reductions were first used by Emil Post in a paper published in 1944. Later Norman Shapiro used the same concept in 1956 under the name strong reducibility.
Definitions
Formal languages
Suppose and are formal languages over the alphabets and , respectively. A many-one reduction from to is a total computable function that has the property that each word is in if and only if is in .
If such a function exists, one says that is many-one reducible or m-reducible to and writes
Subsets of natural numbers
Given two sets one says is many-one reducible to and writes
if there exists a total computable function with iff .
If the many-one reduction is injective, one speaks of a one-one reduction and writes .
If the one-one reduction is surjective, one says is recursively isomorphic to and writesp.324
Many-one equivalence
If both and , one says is many-one equivalent or m-equivalent to and writes
Many-one completeness (m-completeness)
A set is called many-one complete, or simply m-complete, iff is recursively enumerable and every recursively enumerable set is m-reducible to .
Degrees
The relation indeed is an equivalence, its equivalence classes are called m-degrees and form a poset with the order induced by .p.257
Some properties of the m-degrees, some of which differ from analogous properties of Turing degrees:pp.555--581
There is a well-defined jump operator on the m-degrees.
The only m-degree with jump 0m′ is 0m.
There are m-degrees where there does not exist where .
Every countable linear order with a least element embeds into .
The first order theory of is isomorphic to the theory of second-order arithmetic.
There is a characterization of as the unique poset satisfying several explicit properties of its ideals, a similar characterization has eluded the Turing degrees.pp.574--575
Myhill's isomorphism theorem can be stated as follows: "For all sets of natural numbers, ." As a corollary, and have the same equivalence classes.p.325 The equivalences classes of are called the 1-degrees.
Many-one reductions with resource limitations
Many-one reductions are often subjected to resource restrictions, for example that the reduction function is computable in polynomial time, logarithmic space, by or circuits, or polylogarithmic projections where each subsequent reduction notion is weaker than the prior; see polynomial-time reduction and log-space reduction for details.
Given decision problems and and an algorithm N that solves instances of , we can use a many-one reduction from to to solve instances of in:
the time needed for N plus the time needed for the reduction
the maximum of the space needed for N and the space needed for the reduction
We say that a class C of languages (or a subset of the power set of the natural numbers) is closed under many-one reducibility if there exists no reduction from a language outside C to a language in C. If a class is closed under many-one reducibility, then many-one reduction can be used to show that a problem is in C by reducing it to a problem in C. Many-one reductions are valuable because most well-studied complexity classes are closed under some type of many-one reducibility, including P, NP, L, NL, co-NP, PSPACE, EXP, and many others. It is known for example that the first four listed are closed up to the very weak reduction notion of polylogarithmic time projections. These classes are not closed under arbitrary many-one reductions, however.
Many-one reductions extended
One may also ask about generalized cases of many-one reduction. One such example is e-reduction, where we consider that are recursively enumerable instead of restricting to recursive . The resulting reducibility relation is denoted , and its poset has been studied in a similar vein to that of the Turing degrees. For example, there is a jump set for e-degrees. The e-degrees do admit some properties differing from those of the poset of Turing degrees, e.g. an embedding of the diamond graph into the degrees below .
Properties
The relations of many-one reducibility and 1-reducibility are transitive and reflexive and thus induce a preorder on the powerset of the natural numbers.
if and only if
A set is many-one reducible to the halting problem if and only if it is recursively enumerable. This says that with regards to many-one reducibility, the halting problem is the most complicated of all recursively enumerable problems. Thus the halting problem is r.e. complete. Note that it is not the only r.e. complete problem.
The specialized halting problem for an individual Turing machine T (i.e., the set of inputs for which T eventually halts) is many-one complete iff T is a universal Turing machine. Emil Post showed that there exist recursively enumerable sets that are neither decidable nor m-complete, and hence that there exist nonuniversal Turing machines whose individual halting problems are nevertheless undecidable.
Karp reductions
A polynomial-time many-one reduction from a problem A to a problem B (both of which are usually required to be decision problems) is a polynomial-time algorithm for transforming inputs to problem A into inputs to problem B, such that the transformed problem has the same output as the original problem. An instance x of problem A can be solved by applying this transformation to produce an instance y of problem B, giving y as the input to an algorithm for problem B, and returning its output. Polynomial-time many-one reductions may also be known as polynomial transformations or Karp reductions, named after Richard Karp. A reduction of this type is denoted by or .
References
Reduction (complexity) | Many-one reduction | [
"Mathematics"
] | 1,528 | [
"Reduction (complexity)",
"Functions and mappings",
"Mathematical relations",
"Mathematical objects"
] |
363,092 | https://en.wikipedia.org/wiki/Million%20years%20ago | Million years ago, abbreviated as Mya, Myr (megayear) or Ma (megaannum), is a unit of time equal to (i.e. years), or approximately 31.6 teraseconds.
Usage
Myr is in common use in fields such as Earth science and cosmology. Myr is also used with Mya or Ma. Together they make a reference system, one to a quantity, the other to a particular point in a year numbering system that is time before the present.
Myr is deprecated in geology, but in astronomy Myr is standard. Where "myr" is seen in geology, it is usually "Myr" (a unit of mega-years). In astronomy, it is usually "Myr" (Million years).
Debate
In geology, a debate remains open concerning the use of Myr (duration) plus Mya (million years ago) versus using only the term Ma. In either case, the term Ma is used in geology literature conforming to ISO 31-1 (now ISO 80000-3) and NIST 811 recommended practices. Traditional style geology literature is written:
The "ago" is implied, so that any such year number "X Ma" between 66 and 145 is "Cretaceous", for good reason. But the counter argument is that having myr for a duration and Mya for an age mixes unit systems, and tempts capitalization errors: "million" need not be capitalized, but "mega" must be; "ma" would technically imply a milliyear (a thousandth of a year, or 8 hours). On this side of the debate, one avoids myr and simply adds ago explicitly (or adds BP), as in:
In this case, "79 Ma" means only a quantity of 79 million years, without the meaning of "79 million years ago".
See also
Billion years ago
Kyr
Megaannum (Ma)
Symbols y and yr
References
Units of time
Units of measurement in astronomy
Geology
uk:Одиниці_вимірювання_часу#Мегарік_і_гігарік | Million years ago | [
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363,188 | https://en.wikipedia.org/wiki/NetWare | NetWare is a discontinued computer network operating system developed by Novell, Inc. It initially used cooperative multitasking to run various services on a personal computer, using the IPX network protocol. The final update release was version 6.5SP8 in May 2009, and it has since been replaced by Open Enterprise Server.
The original NetWare product in 1983 supported clients running both CP/M and MS-DOS, ran over a proprietary star network topology and was based on a Novell-built file server using the Motorola 68000 processor. The company soon moved away from building its own hardware, and NetWare became hardware-independent, running on any suitable Intel-based IBM PC compatible system, and able to utilize a wide range of network cards. From the beginning NetWare implemented a number of features inspired by mainframe and minicomputer systems that were not available in its competitors' products.
In 1991, Novell introduced cheaper peer-to-peer networking products for DOS and Windows, unrelated to their server-centric NetWare. These are NetWare Lite 1.0 (NWL), and later Personal NetWare 1.0 (PNW) in 1993. In 1993, the main NetWare product line took a dramatic turn when version 4 introduced NetWare Directory Services (NDS, later renamed eDirectory), a global directory service based on ISO X.500 concepts (six years later, Microsoft released Active Directory). The directory service, along with a new e-mail system (GroupWise), application configuration suite (ZENworks), and security product (BorderManager) were all targeted at the needs of large enterprises.
By 2000, however, Microsoft was taking more of Novell's customer base and Novell increasingly looked to a future based on a Linux kernel. The successor to NetWare, Open Enterprise Server (OES), released in March 2005, offers all the services previously hosted by NetWare 6.5, but on a SUSE Linux Enterprise Server; the NetWare kernel remained an option until OES 11 in late 2011. NetWare 6.5SP8 General Support ended in 2010; Extended Support was available until the end of 2015, and Self Support until the end of 2017.
History
NetWare evolved from a very simple concept: file sharing instead of disk sharing. By controlling access at the level of individual files, instead of entire disks, files could be locked and better access control implemented. In 1983 when the first versions of NetWare originated, all other competing products were based on the concept of providing shared direct disk access. Novell's alternative approach was validated by IBM in 1984, which helped promote the NetWare product.
Novell NetWare shares disk space in the form of NetWare volumes, comparable to logical volumes. Client workstations running DOS run a special terminate and stay resident (TSR) program that allows them to map a local drive letter to a NetWare volume. Clients log into a server in order to be allowed to map volumes, and access can be restricted according to the login name. Similarly, they can connect to shared printers on the dedicated print server, and print as if the printer is connected locally.
At the end of the 1990s, with Internet connectivity booming, the Internet's TCP/IP protocol became dominant on LANs. Novell had introduced limited TCP/IP support in NetWare 3.x () and 4.x (), consisting mainly of FTP services and UNIX-style LPR/LPD printing (available in NetWare 3.x), and a Novell-developed webserver (in NetWare 4.x). Native TCP/IP support for the client file and print services normally associated with NetWare was introduced in NetWare 5.0 (released in 1998). There was also a short-lived product, NWIP, that encapsulated IPX in TCP/IP, intended to ease transition of an existing NetWare environment from IPX to IP.
During the early to mid-1980s Microsoft introduced their own LAN system in LAN Manager, based on the competing NBF protocol. Early attempts to compete with NetWare failed, but this changed with the inclusion of improved networking support in Windows for Workgroups, and then the successful Windows NT and Windows 95. NT, in particular, offered a sub-set of NetWare's services, but on a system that could also be used on a desktop, and due to the vertical integration there was no need for a third-party client.
Early years
NetWare originated from consulting work by SuperSet Software, a group founded by the friends Drew Major, Dale Neibaur, Kyle Powell and later Mark Hurst. This work stemmed from their classwork at Brigham Young University in Provo, Utah, starting in October 1981.
In 1981, Raymond Noorda engaged the work by the SuperSet team. The team was originally assigned to create a CP/M disk sharing system to help network the Motorola 68000-based hardware that Novell sold at the time. The first S-Net is CP/M-68K-based and shares a hard disk. In 1983, the team was privately convinced that CP/M was a doomed platform and instead came up with a successful file-sharing system for the newly introduced IBM-compatible PC. They also wrote an application called Snipes – a text-mode game – and used it to test the new network and demonstrate its capabilities. Snipes [aka 'NSnipes' for 'Network Snipes'] is the first network application ever written for a commercial personal computer, and it is recognized as one of the precursors of many popular multiplayer games such as Doom and Quake.
First called ShareNet or S-Net, this network operating system (NOS) was later called Novell NetWare. NetWare is based on the NetWare Core Protocol (NCP), which is a packet-based protocol that enables a client to send requests to and receive replies from a NetWare server. Initially, NCP was directly tied to the IPX/SPX protocol, and NetWare communicated natively using only IPX/SPX.
The first product to bear the NetWare name was released in 1983. The original product, NetWare 68 (AKA S-Net), ran on Novell's proprietary 68000-based file server hardware, and used a star network topology. This was later joined by NetWare 86, which could use conventional Intel 8086-based PCs for the server. This was replaced in 1985 with Advanced NetWare 86, which allowed more than one server on the same network. In 1986, after the Intel 80286 processor became available, Novell released Advanced NetWare 286. Two versions were offered for sale; the basic version was sold as ELS I, plus an enhanced version, ELS II. *ELS* stood for "Entry Level System".
NetWare 286 2.x
Advanced NetWare version 2.x, launched in 1986, was written for the then-new 80286 CPU. The 80286 CPU features a new 16-bit protected mode that provides access to up to 16 MiB RAM as well as new mechanisms to aid multi-tasking. (Prior to the 80286, PC CPU servers used the Intel 8088/8086 8-/16-bit processors, which are limited to an address space of 1 MiB with not more than 640 KiB of directly addressable RAM.) The combination of a higher 16 MiB RAM limit, 80286 processor feature utilization, and 256 MB NetWare volume size limit (compared to the 32 MB that DOS allowed at that time) allowed the building of reliable, cost-effective server-based local area networks for the first time. The 16 MiB RAM limit was especially important, since it makes enough RAM available for disk caching to significantly improve performance. This became the key to Novell's performance while also allowing larger networks to be built.
In a significant innovation, NetWare 286 is also hardware-independent, unlike competing network server systems. Novell servers can be assembled using any brand system with an Intel 80286 CPU, any MFM, RLL, ESDI, or SCSI hard drive and any 8- or 16-bit network adapter for which NetWare drivers are available – and 18 different manufacturer's network cards were supported at launch.
The server could support up to four network cards, and these can be a mixture of technologies such as ARCNET, Token Ring and Ethernet. The operating system is provided as a set of compiled object modules that required configuration and linking. Any change to the operating system requires a re-linking of the kernel. Installation also requires the use of a proprietary low-level format program for MFM hard drives called COMPSURF.
The file system used by NetWare 2.x is NetWare File System 286, or NWFS 286, supporting volumes of up to 256 MB. NetWare 286 recognizes 80286 protected mode, extending NetWare's support of RAM from 1 MiB to the full 16 MiB addressable by the 80286. A minimum of 2 MiB is required to start up the operating system; any additional RAM is used for FAT, DET and file caching. Since 16-bit protected mode is implemented in the 80286 and every subsequent Intel x86 processor, NetWare 286 version 2.x will run on any 80286 or later compatible processor.
NetWare 2.x implements a number of features inspired by mainframe and minicomputer systems that were not available in other operating systems of the day. The System Fault Tolerance (SFT) features includes standard read-after-write verification (SFT-I) with on-the-fly bad block re-mapping (at the time, disks did not have that feature built in) and software RAID1 (disk mirroring, SFT-II). The Transaction Tracking System (TTS) optionally protects files against incomplete updates. For single files, this requires only a file attribute to be set. Transactions over multiple files and controlled roll-backs are possible by programming to the TTS API.
NetWare 286 2.x normally requires a dedicated PC to act as the server, where the server uses DOS only as a boot loader to execute the operating system file . All memory is allocated to NetWare; no DOS ran on the server. However, a "non-dedicated" version was also available for price-conscious customers. In this, DOS 3.3 or higher remains in memory, and the processor time-slices between the DOS and NetWare programs, allowing the server computer to be used simultaneously as a network file server and as a user workstation. Because all extended memory (RAM above 1 MiB) is allocated to NetWare, DOS is limited to only 640 KiB; expanded memory managers that used the MMU of 80386 and higher processors, such as EMM386, do not work; 8086-style expanded memory on dedicated plug-in cards is possible however. Time slicing is accomplished using the keyboard interrupt, which requires strict compliance with the IBM PC design model, otherwise performance is affected.
Server licensing on early versions of NetWare 286 is accomplished by using a key card. The key card was designed for an 8-bit ISA bus, and has a serial number encoded on a ROM chip. The serial number has to match the serial number of the NetWare software running on the server. To broaden the hardware base, particularly to machines using the IBM MCA bus, later versions of NetWare 2.x do not require the key card; serialised license floppy disks are used in place of the key cards.
Licensing is normally for 100 users, but two ELS versions were also available. First a 5-user ELS in 1987, and followed by the 8-user ELS 2.12 II in 1988.
NetWare 3.x
NetWare's 3.x range was a major step forward. It began with version 3.0 in 1990, followed quickly by version 3.10 and 3.11 in 1991.
A key feature was support for 32-bit protected mode, eliminating the 16 MiB memory limit of NetWare 286 and therefore allowing larger hard drives to be supported (since NetWare 3.x cached the entire file allocation table and directory entry table into memory for improved performance).
NetWare version 3.x was also much simpler to install, with disk and network support provided by software modules called a NetWare Loadable Module (NLM) loaded either at start-up or when it was needed. NLMs could also add functionality such as anti-virus software, backup software, database and web servers. Support for long filenames was also provided by an NLM.
A new file system was introduced by NetWare 3.x – "NetWare File System 386", or NWFS 386, which significantly extended volume capacity (1 TB, 4 GB files), and could handle up to 16 volume segments spanning multiple physical disk drives. Volume segments could be added while the server was in use and the volume was mounted, allowing a server to be expanded without interruption.
In NetWare 386 3.x all NLMs ran on the server at the same level of processor memory protection, known as "ring 0". This provided the best possible performance, it sacrificed reliability because there was no memory protection, and furthermore NetWare 3.x used a co-operative multitasking model, meaning that an NLM was required to yield to the kernel regularly. For either of these reasons a badly behaved NLM could result in a fatal (ABEND) error.
NetWare continued to be administered using console-based utilities.
With version 3.x, Novell increased the rigors of compatibility testing with their third-party vendors, revamping their certification program in October 1992 and unveiling a two-tier cooperating marketing program. The first tier provided Novell's vendors a package containing a compatibility guideline book, engineering support lines, self-testing tools, and limited marketing resources, the latter including a license to promote products with a logo stating "Yes, it runs with NetWare" – all free of charge and followed at the vendors' discretion. The second tier required a one-time application fee of $7,000 but replaced the logo's byline with a more confident-sounding "Yes, it's NetWare tested and approved" and accorded partners with more extensive support, including on-location testing by Novell Labs. Initially limited to the United States, this program was rolled out in the United Kingdom in the following year.
For a while, Novell also marketed an OEM version of NetWare 3, called Portable NetWare. Originally announced in 1989 by Prime Computer as a product for its Prime EXL range, along with a distinct product for Unix System V, Novell attracted support from a number of other OEMs including Data General, Hewlett-Packard, NCR Corporation, Sun Microsystems and Unisys. An implementation provided by Altos was described in one review as "NetWare 386 for PC Unix systems", running in the standard Unix environment, utilising the native filesystem and network interfaces. Portable NetWare's primary purpose was to offer file and print sharing facilities, but a "native" port of Netware to other platforms was considered necessary to offer the broader feature set of Novell's traditional NetWare products. Alongside Hewlett-Packard, IBM collaborated with Novell to offer Portable NetWare and more comprehensive "native" ports of NetWare for its platforms. Portable NetWare was later known as NetWare for UNIX. As a version of NetWare written in the C programming language, Novell would port functionality from its traditional product to a reference platform, leaving OEMs to port the Novell source code to run on top of their own, typically Unix, operating systems.
While NetWare 3.x was current, Novell introduced its first high-availability clustering system, named NetWare SFT-III, which allowed a logical server to be completely mirrored to a separate physical machine. Implemented as a shared-nothing cluster, under SFT-III the OS was logically split into an interrupt-driven I/O engine and the event-driven OS core. The I/O engines serialized their interrupts (disk, network etc.) into a combined event stream that was fed to two identical copies of the system engine through a fast (typically 100 Mbit/s) inter-server link. Because of its non-preemptive nature, the OS core, stripped of non-deterministic I/O, behaves deterministically, like a large finite-state machine. The outputs of the two system engines were compared to ensure proper operation, and two copies fed back to the I/O engines. Using the existing SFT-II software RAID functionality present in the core, disks could be mirrored between the two machines without special hardware. The two machines could be separated as far as the server-to-server link would permit. In case of a server or disk failure, the surviving server could take over client sessions transparently after a short pause since it had full state information. SFT-III was the first NetWare version able to make use of SMP hardware – the I/O engine could optionally be run on its own CPU. NetWare SFT-III, ahead of its time in several ways, was a mixed success.
With NetWare 3 an improved routing protocol, NetWare Link Services Protocol, has been introduced which scales better than Routing Information Protocol and allows building large networks.
NetWare 4.x
Version 4 in 1993 introduced NetWare Directory Services, later re-branded as Novell Directory Services (NDS), based on X.500, which replaced the Bindery with a global directory service, in which the infrastructure was described and managed in a single place. Additionally, NDS provided an extensible schema, allowing the introduction of new object types. This allowed a single user authentication to NDS to govern access to any server in the directory tree structure. Users could therefore access network resources no matter on which server they resided, although user license counts were still tied to individual servers. (Large enterprises could opt for a license model giving them essentially unlimited per-server users if they let Novell audit their total user count.)
Version 4 also introduced a number of useful tools and features, such as transparent compression at file system level and RSA public/private encryption.
Another new feature was the NetWare Asynchronous Services Interface (NASI). It allowed network sharing of multiple serial devices, such as modems. Client port redirection occurred via a DOS or Windows driver allowing companies to consolidate modems and analog phone lines.
NetWare for OS/2
Promised as early as 1988, when the Microsoft-IBM collaboration was still ongoing and OS/2 1.x was still a 16-bit product, the product didn't become commercially available until after IBM and Microsoft had parted ways and OS/2 2.0 had become a 32-bit, pre-emptive multitasking and multithreading OS.
By August 1993, Novell released its first version of "NetWare for OS/2". This first release supported OS/2 2.1 (1993) as the base OS, and required that users first buy and install IBM OS/2, then purchase NetWare 4.01, and then install the NetWare for OS/2 product. It retailed for $200.
By around 1995, and coincidental with IBM's renewed marketing push for its 32-bit OS/2 Warp OS, both as a desktop client and as a LAN server (OS/2 Warp Server), NetWare for OS/2 began receiving some good press coverage. "NetWare 4.1 for OS/2" allowed to run Novell's network stack and server modules on top of IBM's 32-bit kernel and network stack. It was basically NetWare 4.x running as a service on top of OS/2. It was compatible with third party client and server utilities and NetWare Loadable Modules.
Since IBM's 32-bit OS/2 included Netbios, IPX/SPX and TCP/IP support, this means that sysadmins could run all three most popular network stacks on a single box, and use the OS/2 box as a workstation too. NetWare for OS/2 shared memory on the system with OS/2 seamlessly. The book "Client Server survival Guide with OS/2" described it as "glue code that lets the unmodified NetWare 4.x server program think it owns all resources on a OS/2 system". It also claimed that a NetWare server running on top of OS/2 only suffered a 5% to 10% overhead over NetWare running over the bare metal hardware, while gaining OS/2's pre-emptive multitasking and object oriented GUI.
Novell continued releasing bugfixes and updates to NetWare for OS/2 up to 1998.
Strategic mistakes
Novell's strategy with NetWare 286 2.x and 3.x proved very successful; before the arrival of Windows NT Server, Novell claimed 90% of the market for PC based servers.
However, the design of NetWare 3.x and later involved a DOS partition to load NetWare server files. While of little technical import, this feature became a liability due to the system administration it required. Compounding this, the NetWare console remained text-based at a time the Windows graphical interface gained widespread acceptance. Especially new users preferred the Windows graphical interface to learning DOS commands necessary to build and control a NetWare server.
Novell could have eliminated at least the separately bootable DOS partition requirement at the outset, by retaining the design of NetWare 286, which installed the server file into a Novell partition and allowed the server to boot from the Novell partition without creating a bootable DOS partition. Novell finally added support for this in a Support Pack for NetWare 6.5.
As Novell initially used IPX/SPX instead of TCP/IP, they were poorly positioned to take advantage of the Internet in 1995. This resulted in Novell servers being bypassed for routing and Internet access in favor of hardware routers, Unix-based operating systems such as FreeBSD, and SOCKS and HTTP Proxy Servers on Windows and other operating systems.
A decision by the management of Novell also took away the ability of independent resellers and engineers to recommend and sell the product. The reduction of their effective sales force created this downward spiral in sales.
NetWare 4.1x and NetWare for Small Business
Novell priced NetWare 4.10 similarly to NetWare 3.12, allowing customers who resisted NDS (typically small businesses) to try it at no cost.
Later Novell released NetWare version 4.11 in 1996 which included many enhancements that made the operating system easier to install, easier to operate, faster, and more stable. It also included the first full 32-bit client for Microsoft Windows-based workstations, SMP support and the NetWare Administrator (NWADMIN or NWADMN32), a GUI-based administration tool for NetWare. Previous administration tools used the Cworthy interface, the character-based GUI tools such as SYSCON and PCONSOLE with blue text-based background. Some of these tools survive to this day, for instance MONITOR.NLM.
Novell packaged NetWare 4.11 with its Web server, TCP/IP support and the Netscape browser into a bundle dubbed IntranetWare (also written as intraNetWare). A version designed for networks of 25 or fewer users was named IntranetWare for Small Business and contained a limited version of NDS and tried to simplify NDS administration. The intranetWare name was dropped in NetWare 5.
During this time Novell also began to leverage its directory service, NDS, by tying their other products into the directory. Their e-mail system, GroupWise, was integrated with NDS, and Novell released many other directory-enabled products such as ZENworks and BorderManager.
NetWare still required IPX/SPX as NCP used it, but Novell started to acknowledge the demand for TCP/IP with NetWare 4.11 by including tools and utilities that made it easier to create intranets and link networks to the Internet. Novell bundled tools, such as the IPX/IP gateway, to ease the connection between IPX workstations and IP networks. It also began integrating Internet technologies and support through features such as a natively hosted web server.
NetWare 5.x
With the release of NetWare 5 in October 1998 Novell switched its primary NCP interface from the IPX/SPX network protocol to TCP/IP to meet market demand. Products continued to support IPX/SPX, but the emphasis shifted to TCP/IP. New features included:
a GUI for NetWare
Novell Storage Services (NSS), a file system to replace the traditional NetWare File System (which Novell continued to support)
Java virtual machine for NetWare
Novell Distributed Print Services (NDPS), an infrastructure for printing over networks
ConsoleOne, a Java-based GUI administration console
directory-enabled Public key infrastructure services (PKIS)
directory-enabled DNS and DHCP servers
support for Storage Area Networks (SANs)
Novell Cluster Services (NCS), a replacement for SFT-III
Oracle 8i with a 5-user license
The Cluster Services improved on SFT-III, as NCS did not require specialized hardware or identical server configurations.
Novell released NetWare 5 during a time when NetWare's market share had started dropping precipitously; many companies and organizations replaced their NetWare servers with servers running Microsoft's Windows NT operating system.
Around this time Novell also released their last upgrade to the NetWare 4 operating system, NetWare 4.2.
NetWare 5 and above supported Novell NetStorage for Internet-based access to files stored within NetWare.
Novell released NetWare 5.1 in January 2000. It introduced a number of tools, such as:
IBM WebSphere Application Server
NetWare Management Portal (later called Novell Remote Manager), web-based management of the operating system
FTP, NNTP and streaming-media servers
NetWare Web Search Server
WebDAV support
NetWare 6.0
NetWare 6 was released in October 2001, shortly after its predecessor. This version has a simplified licensing scheme based on users, not server connections. This allows unlimited connections per user to any number of NetWare servers in the network. Novell Cluster Services was also improved to support 32-node clusters; the base NetWare 6.0 product included a two-node clustering license.
NetWare 6.5
NetWare 6.5 was released in August 2003. Some of the new features in this version included:
more open-source products such as PHP, MySQL and OpenSSH
a port of the Bash shell and a lot of traditional Unix utilities such as wget, grep, awk and sed to provide additional capabilities for scripting
iSCSI support (both target and initiator)
Virtual Office – an "out of the box" web portal for end users providing access to e-mail, personal file storage, company address book, etc.
Domain controller functionality
Universal password
DirXML Starter Pack – synchronization of user accounts with another eDirectory tree, a Windows NT domain or Active Directory.
exteNd Application Server – a Java EE 1.3-compatible application server
support for customized printer driver profiles and printer usage auditing
NX bit support
support for USB storage devices
support for encrypted volumes
The latest – and apparently last – Service Pack for NetWare 6.5 is SP8, released May 2009.
Open Enterprise Server
1.0
In 2003, Novell announced the successor product to NetWare: Open Enterprise Server (OES). First released in March 2005, OES completes the separation of the services traditionally associated with NetWare (such as Directory Services, and file-and-print) from the platform underlying the delivery of those services. OES is essentially a set of applications (eDirectory, NetWare Core Protocol services, iPrint, etc.) that can run atop either a Linux or a NetWare kernel platform. Clustered OES implementations can even migrate services from Linux to NetWare and back again, making Novell one of the very few vendors to offer a multi-platform clustering solution.
Consequent to Novell's acquisitions of Ximian and the German Linux distributor SuSE, Novell moved away from NetWare and shifted its focus towards Linux. Marketing was focused on getting faithful NetWare users to move to the Linux platform for future releases. The clearest indication of this direction was Novell's controversial decision to release Open Enterprise Server on Linux only, not NetWare. Novell later watered down this decision and stated that NetWare's 90 million users would be supported until at least 2015. Meanwhile, many former NetWare customers rejected the confusing mix of licensed software running on an open-source Linux operating system in favor of moving to complete Open Source solutions such as those offered by Red Hat.
2.0
OES 2 was released on 8 October 2007. It includes NetWare 6.5 SP7, which supports running as a paravirtualized guest inside the Xen hypervisor and new Linux based version using SLES10.
New features include
64-bit support
Virtualization
Dynamic Storage Technology, which provide Shadow Volumes
Domain services for Windows (provided in OES 2 service pack 1)
From the 1990s
some organizations still used Novell NetWare, but it had started to lose popularity from the mid-1990s, when NetWare was the de facto standard for file- and printer-sharing software for the Intel x86 server platform.
Microsoft successfully took market share from NetWare products from the late-1990s. Microsoft's more aggressive marketing was aimed directly at non-technical management through major magazines, while Novell NetWare's was through more technical magazines read by IT personnel.
Novell did not adapt their pricing structure to current market conditions, and NetWare sales suffered.
NetWare Lite / Personal NetWare
NetWare Lite and Personal NetWare were a series of peer-to-peer networks developed by Novell for DOS- and Windows-based computers aimed at personal users and small businesses between 1991 and 1995.
Performance
NetWare dominated the network operating system (NOS) market from the mid-1980s through the mid- to late-1990s due to its extremely high performance relative to other NOS technologies. Most benchmarks during this period demonstrated a 5:1 to 10:1 performance advantage over products from Microsoft, Banyan, and others. One noteworthy benchmark pitted NetWare 3.x running NFS services over TCP/IP (not NetWare's native IPX protocol) against a dedicated Auspex NFS server and an SCO Unix server running NFS service. NetWare NFS outperformed both 'native' NFS systems and claimed a 2:1 performance advantage over SCO Unix NFS on the same hardware.
The reasons for NetWare's performance advantage are given below.
File service instead of disk service
When first developed, nearly all LAN storage was based on the disk server model. This meant that if a client computer wanted to read a particular block from a particular file it would have to issue the following requests across the relatively slow LAN:
Read first block of directory
Continue reading subsequent directory blocks until the directory block containing the information on the desired file was found, could be many directory blocks
Read through multiple file entry blocks until the block containing the location of the desired file block was found, could be many directory blocks
Read the desired data block
NetWare, since it was based on a file service model, interacted with the client at the file API level:
Send file open request (if this hadn't already been done)
Send a request for the desired data from the file
All of the work of searching the directory to figure out where the desired data was physically located on the disk was performed at high speed locally on the server.
By the mid-1980s, most NOS products had shifted from the disk service to the file service model. Today, the disk service model is making a comeback, see SAN.
Aggressive caching
From the start, the NetWare design focused on servers with copious amounts of RAM. The entire file allocation table (FAT) was read into RAM when a volume was mounted, thereby requiring a minimum amount of RAM proportional to online disk space; adding a disk to a server would often require a RAM upgrade as well. Unlike most competing network operating systems prior to Windows NT, NetWare automatically used all otherwise unused RAM for caching active files, employing delayed write-backs to facilitate re-ordering of disk requests (elevator seeks). An unexpected shutdown could therefore corrupt data, making an uninterruptible power supply practically a mandatory part of a server installation.
The default dirty cache delay time was fixed at 2.2 seconds in NetWare 286 versions 2.x. Starting with NetWare 386 3.x, the dirty disk cache delay time and dirty directory cache delay time settings controlled the amount of time the server would cache changed ("dirty") data before saving (flushing) the data to a hard drive. The default setting of 3.3 seconds could be decreased to 0.5 seconds but not reduced to zero, while the maximum delay was 10 seconds. The option to increase the cache delay to 10 seconds provided a significant performance boost. Windows 2000 and 2003 server do not allow adjustment to the cache delay time. Instead, they use an algorithm that adjusts cache delay.
Efficiency of NetWare Core Protocol (NCP)
Most network protocols in use at the time NetWare was developed didn't trust the network to deliver messages. A typical client file read would work something like this:
Client sends read request to server
Server acknowledges request
Client acknowledges acknowledgement
Server sends requested data to client
Client acknowledges data
Server acknowledges acknowledgement
In contrast, NCP was based on the idea that networks worked perfectly most of the time, so the reply to a request served as the acknowledgement. Here is an example of a client read request using this model:
Client sends read request to server
Server sends requested data to client
All requests contained a sequence number, so if the client didn't receive a response within an appropriate amount of time it would re-send the request with the same sequence number. If the server had already processed the request it would resend the cached response, if it had not yet had time to process the request it would only send a "positive acknowledgement". The bottom line to this 'trust the network' approach was a 2/3 reduction in network transactions and the associated latency.
Non-preemptive OS designed for network services
One of the raging debates of the 1990s was whether it was more appropriate for network file service to be performed by a software layer running on top of a general purpose operating system, or by a special purpose operating system. NetWare was a special purpose operating system, not a timesharing OS. It was written from the ground up as a platform for client-server processing services. Initially it focused on file and print services, but later demonstrated its flexibility by running database, email, web and other services as well. It also performed efficiently as a router, supporting IPX, TCP/IP, and Appletalk, though it never offered the flexibility of a 'hardware' router.
In 4.x and earlier versions, NetWare did not support preemption, virtual memory, graphical user interfaces, etc. Processes and services running under the NetWare OS were expected to be cooperative, that is to process a request and return control to the OS in a timely fashion. On the down side, this trust of application processes to manage themselves could lead to a misbehaving application bringing down the server.
See also
Novell NetWare Access Server (NAS)
Comparison of operating systems
Btrieve
NCOPY
Notes
References
Further reading
External links
NetWare Cool Solutions – Tips & tricks, guides, tools and other resources submitted by the NetWare community
Another brief history of NetWare
1983 software
Network operating systems
NetWare
Proprietary software
X86 operating systems
PowerPC operating systems
MIPS operating systems
Discontinued operating systems | NetWare | [
"Engineering"
] | 7,497 | [
"Computer networks engineering",
"Network operating systems"
] |
363,196 | https://en.wikipedia.org/wiki/Sleeping%20barber%20problem | In computer science, the sleeping barber problem is a classic inter-process communication and synchronization problem that illustrates the complexities that arise when there are multiple operating system processes.
The problem was originally proposed in 1965 by computer science pioneer Edsger Dijkstra, who used it to make the point that general semaphores are often superfluous.
Problem statement
Imagine a hypothetical barbershop with one barber, one barber chair, and a waiting room with n chairs (n may be 0) for waiting customers. The following rules apply:
If there are no customers, the barber falls asleep in the chair
A customer must wake the barber if he is asleep
If a customer arrives while the barber is working, the customer leaves if all chairs are occupied and sits in an empty chair if it's available
When the barber finishes a haircut, he inspects the waiting room to see if there are any waiting customers and falls asleep if there are none
There are two main complications. First, there is a risk that a race condition, where the barber sleeps while a customer waits for the barber to get them for a haircut, arises because all of the actions—checking the waiting room, entering the shop, taking a waiting room chair—take a certain amount of time. Specifically, a customer may arrive to find the barber cutting hair so they return to the waiting room to take a seat but while walking back to the waiting room the barber finishes the haircut and goes to the waiting room, which he finds empty (because the customer walks slowly or went to the restroom) and thus goes to sleep in the barber chair. Second, another problem may occur when two customers arrive at the same time when there is only one empty seat in the waiting room and both try to sit in the single chair; only the first person to get to the chair will be able to sit.
A multiple sleeping barbers problem has the additional complexity of coordinating several barbers among the waiting customers.
Solutions
There are several possible solutions, but all solutions require a mutex, which ensures that only one of the participants can change state at once. The barber must acquire the room status mutex before checking for customers and release it when they begin either to sleep or cut hair; a customer must acquire it before entering the shop and release it once they are sitting in a waiting room or barber chair, and also when they leave the shop because no seats were available. This would take care of both of the problems mentioned above. A number of semaphores is also required to indicate the state of the system. For example, one might store the number of people in the waiting room.
Implementation
The following pseudocode guarantees synchronization between barber and customer and is deadlock free, but may lead to starvation of a customer. The problem of starvation can be solved with a first-in first-out (FIFO) queue. The semaphore would provide two functions: wait() and signal(), which in terms of C code would correspond to P() and V(), respectively.
# The first two are mutexes (only 0 or 1 possible)
Semaphore barberReady = 0
Semaphore accessWRSeats = 1 # if 1, the number of seats in the waiting room can be incremented or decremented
Semaphore custReady = 0 # the number of customers currently in the waiting room, ready to be served
int numberOfFreeWRSeats = N # total number of seats in the waiting room
def Barber():
while true: # Run in an infinite loop.
wait(custReady) # Try to acquire a customer - if none is available, go to sleep.
wait(accessWRSeats) # Awake - try to get access to modify # of available seats, otherwise sleep.
numberOfFreeWRSeats += 1 # One waiting room chair becomes free.
signal(barberReady) # I am ready to cut.
signal(accessWRSeats) # Don't need the lock on the chairs anymore.
# (Cut hair here.)
def Customer():
while true: # Run in an infinite loop to simulate multiple customers.
wait(accessWRSeats) # Try to get access to the waiting room chairs.
if numberOfFreeWRSeats > 0: # If there are any free seats:
numberOfFreeWRSeats -= 1 # sit down in a chair
signal(custReady) # notify the barber, who's waiting until there is a customer
signal(accessWRSeats) # don't need to lock the chairs anymore
wait(barberReady) # wait until the barber is ready
# (Have hair cut here.)
else: # otherwise, there are no free seats; tough luck --
signal(accessWRSeats) # but don't forget to release the lock on the seats!
# (Leave without a haircut.)
See also
Dining philosophers problem
Cigarette smokers problem
Producers-consumers problem
Readers–writers problem
References
Concurrency (computer science)
Edsger W. Dijkstra
Articles with example pseudocode
Problems in computer science | Sleeping barber problem | [
"Technology"
] | 1,051 | [
"Problems in computer science",
"Computer science"
] |
363,198 | https://en.wikipedia.org/wiki/The%20East%20Is%20Red%20%28song%29 | "The East Is Red" is a Chinese Communist Party revolutionary song that was the de facto national anthem of the People's Republic of China during the Cultural Revolution in the 1960s. The lyrics of the song were attributed to Li Youyuan (李有源), a farmer from Shaanbei (northern Shaanxi), and the melody was derived from a local peasant love song from the Loess Plateau entitled "Bai Ma Diao" (《白马调》, White Horse Tune), also known as "Zhima You" (《芝麻油》, Sesame Oil), which was widely circulated in the area around Yan'an in the 1930s. The farmer allegedly got his inspiration upon seeing the rising sun in the morning of a sunny day.
History
Early history
The lyrics to "The East Is Red" were adapted from an old Shaanxi folk song about love. The lyrics were often changed depending on the singer. The modern lyrics (attributed to Li Youyuan, a farmer from northern Shaanxi) were produced in 1942 during the Second Sino-Japanese War. It is possible that there was an earlier version that referenced Liu Zhidan (a local communist hero), who was killed in Shanxi in 1936. Later, Mao's name replaced Liu's in the lyrics. The song was popular in the Communist base-area of Yan'an, but became less popular after the Chinese Communist Party (CCP) won the Chinese Civil War and established the People's Republic of China in 1949, possibly because some senior CCP leaders disagreed with the song's portrayal of Mao Zedong as "China's savior".
The lyrics of "The East Is Red" idealize Mao Zedong, and Mao's popularization of "The East Is Red" was one of his earliest efforts to promote his image as a perfect hero in Chinese popular culture after the Korean War. In 1956, a political commissar suggested to China's defense minister, Peng Dehuai, that the song be taught to Chinese troops, but Peng opposed Mao's propaganda, saying "That is a personality cult! That is idealism!" Peng's opposition to "The East Is Red", and to Mao's incipient personality cult in general, contributed to Mao purging Peng in 1959. After Peng was purged, Mao accelerated his efforts to build his personality cult; by 1966, he succeeded in having "The East Is Red" sung in place of China's national anthem in an unofficial capacity.
In 1964, Zhou Enlai used "The East Is Red" as the central chorus for a play he created to promote the personality cult of Mao Zedong, with "March Forward under the Banner of Mao Zedong Thought" as the original title. Zhou also served as co-producer, head writer and director of the play. The central theme of the play was that Mao was the only person capable of leading the CCP to victory. The play was performed by 2,000 artists, and was accompanied by a 1,000-strong chorus and orchestra. It was staged repeatedly in Beijing at the Great Hall of the People in order to ensure that all residents would be able to see it (this was in time for the 15th National Day of the People's Republic of China), and was later adapted into a feature film, also titled "The East Is Red," that was shown all over China. It was in this play that the definite version of the song was heard for the first time; this would be the version used in events during the Cultural Revolution until 1969.
During the Cultural Revolution, Tian Han, the author of China's official national anthem, "March of the Volunteers", was purged; as a result, that song was rarely used. "The East Is Red" was used as China's unofficial national anthem during this time. The song was played through PA systems in towns and villages across China at dawn and at dusk. The Custom House on the Bund in Shanghai still plays the song in place of the Westminster Chimes that were originally played by the British. The Central People's Broadcasting Station began broadcasts every day by playing the song on a set of bronze bells that had been cast over 2,000 years earlier during the Warring States period. Radio and television broadcasts nationwide usually began with the song "The East Is Red" in the morning or at early evening, and ended with the song "The Internationale". In 1967, the commune (now township) of Ujme in Akto County, Kizilsu, Xinjiang was renamed Dongfanghong Commune (literally "The East Is Red Commune": ).
Students were obliged to sing the song in unison every morning at the beginning of the first class of the day. In 1969, the tune was used in the Yellow River Piano Concerto. The Concerto was produced by Jiang Qing and adapted from the Yellow River Cantata by Xian Xinghai. When she adapted the Cantata, Jiang added the tune to "The East Is Red" in order to connect the Concerto with the themes of the Cultural Revolution. After China launched its first satellite in 1970, "The East Is Red" was the first signal the craft sent back to Earth. However, the status of "The East Is Red" as the unofficial national anthem was relinquished in 1978; beginning on October 1 of that year, the current official national anthem, March of the Volunteers, was readopted and played (albeit only in its instrumental version) once again in all national events.
Modern China
Because of its associations with the Cultural Revolution, the song was rarely heard after the rise of Deng Xiaoping in the late 1970s. To this day, the song is considered by some in China to be a somewhat unseemly reminder of the cult of personality associated with Mao. Its official use has largely been replaced by the "March of the Volunteers", whose lyrics mention neither the CCP nor Mao. "The East Is Red" is still commonly heard in recordings played by electronic cigarette lighters bearing Mao's face that are popular with tourists.
The tune of "The East Is Red" remains popular in Chinese popular culture. In 2009, it was voted as the most popular patriotic song in a Chinese government-run internet poll. It is used as the belling melody for striking clocks like Beijing railway station and the Beijing Telegraph Building, Shanghai Customs House as well as the Drum Tower in Xi'an.
Some radio stations in China have used "The East Is Red" as an interval signal, including China Radio International (Indonesian service) and Xinjiang People's Radio Station.
See also
Dong Fang Hong I
Honglaowai
The East Is Red, 1965 film
List of socialist songs
Socialist music from China:
"Ode to the Motherland"
"Socialism is Good"
"Sailing the Seas Depends on the Helmsman"
"Without the Communist Party, There Would Be No New China"
References
External links
Morning Sun
1963 music video of the song
Historical national anthems
Cultural Revolution
Chinese patriotic songs
Maoist China propaganda songs
Asian anthems
Songs about Mao Zedong
Chinese military marches
Culture in Shaanxi
Clocks | The East Is Red (song) | [
"Physics",
"Technology",
"Engineering"
] | 1,451 | [
"Physical systems",
"Machines",
"Clocks",
"Measuring instruments"
] |
363,204 | https://en.wikipedia.org/wiki/Dihedral%20%28aeronautics%29 | Dihedral angle is the upward angle from horizontal of the wings or tailplane of a fixed-wing aircraft. "Anhedral angle" is the name given to negative dihedral angle, that is, when there is a downward angle from horizontal of the wings or tailplane of a fixed-wing aircraft.
Dihedral angle has a strong influence on dihedral effect, which is named after it. Dihedral effect is the amount of roll moment produced in proportion to the amount of sideslip. Dihedral effect is a critical factor in the stability of an aircraft about the roll axis (the spiral mode). It is also pertinent to the nature of an aircraft's Dutch roll oscillation and to maneuverability about the roll axis.
Longitudinal dihedral is a comparatively obscure term related to the pitch axis of an airplane. It is the angle between the zero-lift axis of the wing and the zero-lift axis of the horizontal tail. Longitudinal dihedral can influence the nature of controllability about the pitch axis and the nature of an aircraft's phugoid-mode oscillation.
When the term "dihedral" (of an aircraft) is used by itself it is usually intended to mean "dihedral angle". However, context may otherwise indicate that "dihedral effect" is the intended meaning.
Dihedral angle vs. dihedral effect
Dihedral angle is the upward angle from horizontal of the wings of a fixed-wing aircraft, or of any paired nominally-horizontal surfaces on any aircraft. The term can also apply to the wings of a bird. Dihedral angle is also used in some types of kites such as box kites. Wings with more than one angle change along the full span are said to be polyhedral.
Dihedral angle has important stabilizing effects on flying bodies because it has a strong influence on the dihedral effect.
Dihedral effect of an aircraft is a rolling moment resulting from the vehicle having a non-zero angle of sideslip. Increasing the dihedral angle of an aircraft increases the dihedral effect on it. However, many other aircraft parameters also have a strong influence on dihedral effect. Some of these important factors are: wing sweep, vertical center of gravity, and the height and size of anything on an aircraft that changes its sidewards force as sideslip changes.
Longitudinal dihedral
Dihedral angle on an aircraft almost always implies the angle between two paired surfaces, one on each side of the aircraft. Even then, it is almost always between the left and right wings. However, mathematically dihedral means the angle between any two planes. So, in aeronautics, in one case, the term "dihedral" is applied to mean the difference in angles between two front-to-back surfaces:
Longitudinal dihedral is the difference between the angle of incidence of the wing root chord and angle of incidence of the horizontal tail root chord.
Longitudinal dihedral can also mean the angle between the zero-lift axis of the wing and the zero-lift axis of the horizontal tail instead of between the root chords of the two surfaces. This is the more meaningful usage because the directions of zero-lift are pertinent to trim and stability while the directions of the root chords are not.
This measurement is also often referred to as decalage.
History
In geometry, dihedral angle is the angle between two planes. Aviation usage differs slightly from usage in geometry. In aviation, the usage "dihedral" evolved to mean the positive, up angle between the left and right wings, while usage with the prefix "an-" (as in "anhedral") evolved to mean the negative, down angle between the wings.
The aerodynamic stabilizing qualities of a dihedral angle were described in an influential 1810 article by Sir George Cayley.
Uses of dihedral angle and dihedral effect
Aircraft stability analysis
In analysis of aircraft stability, the dihedral effect is also a stability derivative called Cl meaning the change in rolling moment coefficient (the "Cl") per degree (or radian) of change in sideslip angle (the "").
Provision of stability
The purpose of dihedral effect is to contribute to stability in the roll axis. It is an important factor in the stability of the spiral mode which is sometimes called "roll stability". The dihedral effect does not contribute directly to the restoring of "wings level", but it indirectly helps restore "wings level" through its effect on the spiral mode of motion described below.
Wing clearance
Aircraft designers may increase dihedral angle to provide greater clearance between the wing tips and the runway. This is of particular concern with swept-wing aircraft, whose wingtips could hit the runway on rotation/touchdown. In military aircraft dihedral angle space may be used for mounting materiel and drop-tanks on wing hard points, especially in aircraft with low wings. The increased dihedral effect caused by this design choice may need to be compensated for, perhaps by decreasing the dihedral angle on the horizontal tail.
Using dihedral angle to adjust dihedral effect
During design of a fixed-wing aircraft (or any aircraft with horizontal surfaces), changing dihedral angle is usually a relatively simple way to adjust the overall dihedral effect. This is to compensate for other design elements' influence on the dihedral effect. These other elements (such as wing sweep, vertical mount point of the wing, etc.) may be more difficult to change than the dihedral angle. As a result, differing amounts of dihedral angle can be found on different types of fixed-wing aircraft. For example, the dihedral angle is usually greater on low-wing aircraft than on otherwise-similar high-wing aircraft. This is because "highness" of a wing (or "lowness" of vertical center of gravity compared to the wing) naturally creates more dihedral effect itself. This makes it so less dihedral angle is needed to get the amount of dihedral effect needed.
Common confusions
Dihedral effect is defined simply to be the rolling moment caused by sideslip and nothing else. Rolling moments caused by other things that may be related to sideslip have different names.
Dihedral effect is not caused by yaw rate, nor by the rate of sideslip change. Since dihedral effect is noticed by pilots when "rudder is applied", many pilots and other near-experts explain that the rolling moment is caused by one wing moving more quickly through the air and one wing less quickly. Indeed, these are actual effects, but they are not the dihedral effect, which is caused by being at a sideslip angle, not by getting to one. These other effects are called "rolling moment due to yaw rate" and "rolling moment due to sideslip rate" respectively.
Dihedral effect is not roll stability in and of itself. Roll stability is less-ambiguously termed "spiral mode stability" and dihedral effect is a contributing factor to it.
How dihedral angle creates dihedral effect and stabilizes the spiral mode
The dihedral angle contributes to the total dihedral effect of the aircraft. In turn, the dihedral effect contributes to stability of the spiral mode. A stable spiral mode will cause the aircraft to eventually return to a nominally "wings level" bank angle when the angle of the wings is disturbed to become off-level.
If a disturbance causes an aircraft to roll away from its normal wings-level position as in Figure 1, the aircraft will begin to move somewhat sideways toward the lower wing.
In Figure 2, the airplane's flight path has started to move toward its left while the nose of the airplane is still pointing in the original direction. This means that the oncoming air is arriving somewhat from the left of the nose. The airplane now has sideslip angle in addition to the bank angle. Figure 2 shows the airplane as it presents itself to the oncoming air.
How dihedral angle creates rolling moment from sideslip (dihedral effect)
In Figure 2, the sideslip conditions produce greater angle of attack on the forward-yawed wing and smaller angle of attack on the rearward-yawed wing. This alteration of angle of attack by sideslip is visible in Figure 2. As greater angle of attack produces more lift (in the usual case, when the wing is not near stalling), the forward wing will have more lift and the rearward wing will have less lift. This difference in lift between the wings is a rolling moment, and it is caused by the sideslip. It is a contribution to the total dihedral effect of the aircraft.
How dihedral effect stabilizes the spiral mode
The rolling moment created by the sideslip (labeled as "P") tends to roll the aircraft back to wings level. More dihedral effect tries to roll the wings in the "leveling" direction more strongly, and less dihedral effect tries to roll the wings in the "leveling" direction less strongly. Dihedral effect helps stabilize the spiral mode by tending to roll the wings toward level in proportion to the amount of sideslip that builds up. It is not the whole picture however. At the same time that angle of sideslip is building up, the vertical fin is trying to turn the nose back into the wind, much like a weathervane, minimizing the amount of sideslip that can be present. If there is no sideslip, there can be no restoring rolling moment. If there is less sideslip, there is less restoring rolling moment. Yaw stability created by the vertical fin opposes the tendency for dihedral effect to roll the wings back level by limiting sideslip.
The spiral mode is the tendency to slowly diverge from, or the tendency to slowly return to wings level. If the spiral mode is stable, the aircraft will slowly return to wings-level, if it is unstable, the aircraft will slowly diverge from wings-level. Dihedral effect and yaw stability are the two primary factors that affect the stability of the spiral mode, although there are other factors that affect it less strongly.
Other factors contributing to dihedral effect
Factors of design other than dihedral angle also contribute to dihedral effect. Each increases or decreases total aircraft dihedral effect to a greater or lesser degree.
Sweepback
Wing sweepback also increases the dihedral effect, for roughly 1° of effective dihedral with every 10° of sweepback. This is one reason for anhedral configuration on aircraft with high sweep angle, as well as on some airliners, even on low-wing aircraft such as the Tu-134 and Tu-154.
In any case, wing sweepback can also occur with a dihedral configuration. For instance, two small biplanes produced from the 1930s to 1945 by Bücker Flugzeugbau in Germany, the Bücker Jungmann two-seat trainer and the Bücker Jungmeister aerobatic competition biplane, were designed with sweepbacks of approximately 11 degrees, which provided significant dihedral effect – in addition to their small dihedral angles having a similar but lesser effect.
Vertical position of the center of mass
The center of mass, usually called the center of gravity or "CG", is the balance point of an aircraft. If suspended at this point and allowed to rotate, a body (aircraft) will be balanced. The front-to-back location of the CG is of primary importance for the general stability of the aircraft, but the vertical location has important effects as well.
The vertical location of the CG changes the amount of dihedral effect. As the "vertical CG" moves lower, dihedral effect increases. This is caused by the center of lift and drag being further above the CG and having a longer moment arm. So, the same forces that change as sideslip changes (primarily sideforce, but also lift and drag) produce a larger moment about the CG of the aircraft. This is sometimes referred to as the pendulum effect.
An extreme example of the effect of vertical CG on dihedral effect is a paraglider. The dihedral effect created by the very low vertical CG more than compensates for the negative dihedral effect created by the strong anhedral of the necessarily strongly downward curving wing.
Wing location
The wing location on a fixed-wing aircraft will also influence its dihedral effect. A high-wing configuration provides about 5° of effective dihedral over a low-wing configuration.
Effects of too much dihedral effect
A side effect of too much dihedral effect, caused by excessive dihedral angle among other things, can be yaw-roll coupling (a tendency for an aircraft to Dutch roll). This can be unpleasant to experience, or in extreme conditions it can lead to loss of control or can overstress an aircraft.
Anhedral and polyhedral
Anhedral
Military fighter aircraft often have near zero or even anhedral angle reducing dihedral effect and hence reducing the stability of the spiral mode. This increases maneuverability which is desirable in fighter-type aircraft.
Anhedral angles are also seen on aircraft with a high mounted wing, such as the very large Antonov An-124 and Lockheed C-5 Galaxy cargo aircraft. In such designs, the high mounted wing is above the aircraft's center of gravity which confers extra dihedral effect due to the pendulum effect (also called the keel effect) and so additional dihedral angle is often not required. Such designs can have excessive dihedral effect and so be excessively stable in the spiral mode, so anhedral angle on the wing is added to cancel out some of the dihedral effect so that the aircraft can be more easily maneuvered.
Polyhedral
Most aircraft have been designed with planar wings with simple dihedral (or anhedral). Some older aircraft such as the Beriev Be-12 were designed with gull wings bent near the root. Others, such as the Vought F4U Corsair, used an inverted gull wing design, which allowed for shorter landing struts and extra ground clearance for large propellers and external payloads, such as external fuel tanks or bombs. Modern polyhedral wing designs generally bend upwards near the wingtips (also known as tip dihedral), increasing dihedral effect without increasing the angle the wings meet at the root, which may be restricted to meet other design criteria.
Polyhedral is seen on gliders and some other aircraft. The McDonnell Douglas F-4 Phantom II is one such example, unique among jet fighters for having dihedral wingtips. This was added after flight testing of the flat winged prototype showed the need to correct some unanticipated spiral mode instability – angling the wingtips, which were already designed to fold up for carrier operations, was a more practical solution than re-engineering the entire wing.
References
Footnotes
Notes
External links
Demonstration of dihedral effect on Wolfram Demonstrations Project
Video explanation on Real Engineering YouTube channel
Aircraft aerodynamics
Aircraft configurations
Aircraft wing design
Wing configurations | Dihedral (aeronautics) | [
"Engineering"
] | 3,016 | [
"Aircraft configurations",
"Aerospace engineering"
] |
363,207 | https://en.wikipedia.org/wiki/38%20%28number%29 | 38 (thirty-eight) is the natural number following 37 and preceding 39.
In mathematics
specifically, the 11th discrete Semiprime, it being the 7th of the form (2.q).
the first member of the third cluster of two discrete semiprimes 38, 39 the next such cluster is 57, 58.
with an aliquot sum of 22 in an aliquot sequence of five composite numbers (38,22,14,10,8,7,1,0) to the Prime in the 7-aliquot tree. 38 is the first semiprime within a chain of 4 semiprimes in its aliquot sequence (38,22,14,10). The next semiprime with a four semiprime chain is 166.
38! − 1 yields which is the 16th factorial prime.
There is no answer to the equation φ(x) = 38, making 38 a nontotient.
38 is the sum of the squares of the first three primes.
37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.
38 is the largest even number which cannot be written as the sum of two odd composite numbers.
The sum of each row of the only non-trivial (order 3) magic hexagon is 38.
References
Integers | 38 (number) | [
"Mathematics"
] | 275 | [
"Elementary mathematics",
"Integers",
"Mathematical objects",
"Numbers"
] |
363,218 | https://en.wikipedia.org/wiki/Long%20ton | The long ton, also known as the imperial ton or displacement ton, is a measurement unit equal to 2,240 pounds (1,016.0 kg). It is the name for the unit called the "ton" in the avoirdupois system of weights or Imperial system of measurements. It was standardised in the 13th century. It is used in the United States for bulk commodities.
It is not to be confused with the short ton, a unit of weight equal to used in the United States, and Canada before metrication, also referred to simply as a "ton".
Unit definition
A long ton is defined as exactly 2,240 pounds. The long ton arises from the traditional British measurement system: A long ton is 20 long hundredweight (cwt), each of which is 8 stone Thus, a long ton is
Unit equivalences
A long ton, also called the weight ton (W/T), imperial ton, or displacement ton, is equal to:
exactly 12% more than the 2,000 pounds of the North American short ton, being 20 long hundredweight (112 lb) rather than 20 short hundredweight (100 lb)
the weight of of salt water with a density of
Usage around the world
United Kingdom
To comply with the practices of the European Union, the British Imperial ton was explicitly excluded from use for trade by the United Kingdom's Weights and Measures Act of 1985. The measure used since then is the metric ton of 1,000 kilograms, identified through the word "tonne".
If still used for measurement, then the word "ton" is taken to refer to an imperial or long ton.
United States
In the United States, the long ton is commonly used in measuring the displacement of ships and the shipping of baled commodities and bulk goods like iron ore and elemental sulfur.
International
The long ton was the unit prescribed for warships by the Washington Naval Treaty of 1922; for example, battleships were limited to a displacement of .
The long ton is traditionally used as the unit of weight in international contracts for many bulk goods and commodities.
See also
Short ton, equal to .
Ton
Tonnage, volume measurement used in maritime shipping, originally based on .
Tonne, also known as a metric ton (t), equal to or 1 Mg.
References
Units of mass
Ton, long
Customary units of measurement in the United States | Long ton | [
"Physics",
"Mathematics"
] | 478 | [
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363,225 | https://en.wikipedia.org/wiki/Substitution%20matrix | In bioinformatics and evolutionary biology, a substitution matrix describes the frequency at which a character in a nucleotide sequence or a protein sequence changes to other character states over evolutionary time. The information is often in the form of log odds of finding two specific character states aligned and depends on the assumed number of evolutionary changes or sequence dissimilarity between compared sequences. It is an application of a stochastic matrix. Substitution matrices are usually seen in the context of amino acid or DNA sequence alignments, where they are used to calculate similarity scores between the aligned sequences.
Background
In the process of evolution, from one generation to the next the amino acid sequences of an organism's proteins are gradually altered through the action of DNA mutations. For example, the sequence
ALEIRYLRD
could mutate into the sequence
ALEINYLRD
in one step, and possibly
AQEINYQRD
over a longer period of evolutionary time. Each amino acid is more or less likely to mutate into various other amino acids. For instance, a hydrophilic residue such as arginine is more likely to be replaced by another hydrophilic residue such as glutamine, than it is to be mutated into a hydrophobic residue such as leucine. (Here, a residue refers to an amino acid stripped of a hydrogen and/or a hydroxyl group and inserted in the polymeric chain of a protein.) This is primarily due to redundancy in the genetic code, which translates similar codons into similar amino acids. Furthermore, mutating an amino acid to a residue with significantly different properties could affect the folding and/or activity of the protein. This type of disruptive substitution is likely to be removed from populations by the action of purifying selection because the substitution has a higher likelihood of rendering a protein nonfunctional.
If we have two amino acid sequences in front of us, we should be able to say something about how likely they are to be derived from a common ancestor, or homologous. If we can line up the two sequences using a sequence alignment algorithm such that the mutations required to transform a hypothetical ancestor sequence into both of the current sequences would be evolutionarily plausible, then we'd like to assign a high score to the comparison of the sequences.
To this end, we will construct a 20x20 matrix where the th entry is equal to the probability of the th amino acid being transformed into the th amino acid in a certain amount of evolutionary time. There are many different ways to construct such a matrix, called a substitution matrix. Here are the most commonly used ones:
Identity matrix
The simplest possible substitution matrix would be one in which each amino acid is considered maximally similar to itself, but not able to transform into any other amino acid. This matrix would look like
This identity matrix will succeed in the alignment of very similar amino acid sequences but will be miserable at aligning two distantly related sequences. We need to figure out all the probabilities in a more rigorous fashion. It turns out that an empirical examination of previously aligned sequences works best.
Log-odds matrices
We express the probabilities of transformation in what are called log-odds scores. The scores matrix S is defined as
where is the probability that amino acid transforms into amino acid , and , are the frequencies of amino acids i and j. The base of the logarithm is not important, and the same substitution matrix is often expressed in different bases.
Example matrices
PAM
One of the first amino acid substitution matrices, the PAM (Point Accepted Mutation) matrix was developed by Margaret Dayhoff in the 1970s. This matrix is calculated by observing the differences in closely related proteins. Because the use of very closely related homologs, the observed mutations are not expected to significantly change the common functions of the proteins. Thus the observed substitutions (by point mutations) are considered to be accepted by natural selection.
One PAM unit is defined as 1% of the amino acid positions that have been changed. To create a PAM1 substitution matrix, a group of very closely related sequences with mutation frequencies corresponding to one PAM unit is chosen. Based on collected mutational data from this group of sequences, a substitution matrix can be derived. This PAM1 matrix estimates what rate of substitution would be expected if 1% of the amino acids had changed.
The PAM1 matrix is used as the basis for calculating other matrices by assuming that repeated mutations would follow the same pattern as those in the PAM1 matrix, and multiple substitutions can occur at the same site. With this assumption, the PAM2 matrix can estimated by squaring the probabilities. Using this logic, Dayhoff derived matrices as high as PAM250. Usually the PAM 30 and the PAM70 are used.
BLOSUM
Dayhoff's methodology of comparing closely related species turned out not to work very well for aligning evolutionarily divergent sequences. Sequence changes over long evolutionary time scales are not well approximated by compounding small changes that occur over short time scales. The BLOSUM (BLOck SUbstitution Matrix) series of matrices rectifies this problem. Henikoff & Henikoff constructed these matrices using multiple alignments of evolutionarily divergent proteins. The probabilities used in the matrix calculation are computed by looking at "blocks" of conserved sequences found in multiple protein alignments. These conserved sequences are assumed to be of functional importance within related proteins and will therefore have lower substitution rates than less conserved regions. To reduce bias from closely related sequences on substitution rates, segments in a block with a sequence identity above a certain threshold were clustered, reducing the weight of each such cluster (Henikoff and Henikoff). For the BLOSUM62 matrix, this threshold was set at 62%. Pairs frequencies were then counted between clusters, hence pairs were only counted between segments less than 62% identical. One would use a higher numbered BLOSUM matrix for aligning two closely related sequences and a lower number for more divergent sequences.
It turns out that the BLOSUM62 matrix does an excellent job detecting similarities in distant sequences, and this is the matrix used by default in most recent alignment applications such as BLAST.
Differences between PAM and BLOSUM
PAM matrices are based on an explicit evolutionary model (i.e. replacements are counted on the branches of a phylogenetic tree: maximum parismony), whereas the BLOSUM matrices are based on an implicit model of evolution.
The PAM matrices are based on mutations observed throughout a global alignment, this includes both highly conserved and highly mutable regions. The BLOSUM matrices are based only on highly conserved regions in series of alignments forbidden to contain gaps.
The method used to count the replacements is different: unlike the PAM matrix, the BLOSUM procedure uses groups of sequences within which not all mutations are counted the same.
Higher numbers in the PAM matrix naming scheme denote larger evolutionary distance, while larger numbers in the BLOSUM matrix naming scheme denote higher sequence similarity and therefore smaller evolutionary distance. Example: PAM150 is used for more distant sequences than PAM100; BLOSUM62 is used for closer sequences than BLOSUM50.
Newer matrices
A number of newer substitution matrices have been proposed to deal with inadequacies in earlier designs.
JTT, published in the same year as BLOSOM, also performs clustering and uses an implicit model. This may help reduce the systematic error from maximum parismony (MP), but also wastes sequence information.
WAG (Wheelan And Goldman), published in 2001, uses a maximum likelihood estimating procedure instead of any form of MP. The substitution scores are calculated based on the likelihood of a change considering multiple tree topologies derived using neighbor-joining. The scores correspond to an substitution model which includes also amino-acid stationary frequencies and a scaling factor in the similarity scoring. There are two versions of the matrix: WAG matrix based on the assumption of the same amino-acid stationary frequencies across all the compared protein and WAG* matrix with different frequencies for each of included protein families.
Specialized substitution matrices and their extensions
The real substitution rates in a protein depends not only on the identity of the amino acid, but also on the specific structural or sequence context it is in. Many specialized matrices have been developed for these contexts, such as in transmembrane alpha helices, for combinations of secondary structure states and solvent accessibility states, or for local sequence-structure contexts. These context-specific substitution matrices lead to generally improved alignment quality at some cost of speed but are not yet widely used.
Recently, sequence context-specific amino acid similarities have been derived that do not need substitution matrices but that rely on a library of sequence contexts instead. Using this idea, a context-specific extension of the popular BLAST program has been demonstrated to achieve a twofold sensitivity improvement for remotely related sequences over BLAST at similar speeds (CS-BLAST).
Terminology
Although "transition matrix" is often used interchangeably with "substitution matrix" in fields other than bioinformatics, the former term is problematic in bioinformatics. With regards to nucleotide substitutions, "transition" is also used to indicate those substitutions that are between the two-ring purines (A → G and G → A) or are between the one-ring pyrimidines (C → T and T → C). Because these substitutions do not require a change in the number of rings, they occur more frequently than the other substitutions. "Transversion" is the term used to indicate the slower-rate substitutions that change a purine to a pyrimidine or vice versa (A ↔ C, A ↔ T, G ↔ C, and G ↔ T).
See also
Models of DNA evolution
Substitution model
References
Further reading
External links
PAM Matrix calculator
Bioinformatics
Matrices | Substitution matrix | [
"Mathematics",
"Engineering",
"Biology"
] | 2,003 | [
"Matrices (mathematics)",
"Biological engineering",
"Bioinformatics",
"Mathematical objects"
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363,246 | https://en.wikipedia.org/wiki/Raceme | A raceme () or racemoid is an unbranched, indeterminate type of inflorescence bearing flowers having short floral stalks along the shoots that bear the flowers. The oldest flowers grow close to the base and new flowers are produced as the shoot grows in height, with no predetermined growth limit. Examples of racemes occur on mustard (genus Brassica), radish (genus Raphanus), and orchid (genus Phalaenopsis) plants.
Definition
A raceme or racemoid is an unbranched, indeterminate type of inflorescence bearing pedicellate flowers (flowers having short floral stalks called pedicels) along its axis. In botany, an axis means a shoot, in this case one bearing the flowers. In indeterminate inflorescence-like racemes, the oldest flowers grow close to the base and new flowers are produced as the shoot grows in height, with no predetermined growth limit. A plant that flowers on a showy raceme may have this reflected in its scientific name, e.g. the species Actaea racemosa. A compound raceme, also called a panicle, has a branching main axis. Examples of racemes occur on mustard (genus Brassica) and radish (genus Raphanus) plants.
Spike
A spike is an unbranched, indeterminate inflorescence, similar to a raceme, but bearing sessile flowers (sessile flowers are attached directly, without stalks). Examples occur on Malabar nut (Justicia adhatoda) and chaff flowers (genus Achyranthes). A spikelet can refer to a small spike, although it primarily refers to the ultimate flower cluster unit in grasses (family Poaceae) and sedges (family Cyperaceae), in which case the stalk supporting the cluster becomes the pedicel. A true spikelet comprises one or more florets enclosed by two glumes (sterile bracts), with flowers and glumes arranged in two opposite rows along the spikelet. Examples occur on rice (species Oryza sativa) and wheat (genus Triticum), both grasses.
Catkin
An ament or catkin is very similar to a spike or raceme "but with subtending bracts so conspicuous as to conceal the flowers until pollination, as in the pussy–willow, alder, [and] birch...". These are sometimes called amentaceous plants.
Spadix
A spadix is a form of spike in which the florets are densely crowded along a fleshy axis and enclosed by one or more large, brightly–colored bracts called spathes. Usually the female flowers grow at the base, and male flowers grow above. They are a characteristic of the family Araceae, for example jack–in–the–pulpit (species Arisaema triphyllum) and wild calla (genus Calla).
Examples
Etymology
From classical Latin, a racemus is a cluster of grapes.
See also
Inflorescence
Glossary of botanical terms
References
Flowers
Plant morphology
sv:Blomställning#Typer av blomställningar | Raceme | [
"Biology"
] | 660 | [
"Plant morphology",
"Plants"
] |
363,293 | https://en.wikipedia.org/wiki/List%20of%20craters%20on%20Mercury | This is a list of named craters on Mercury, the innermost planet of the Solar System (for other features, see list of geological features on Mercury). Most Mercurian craters are named after famous writers, artists and composers. According to the rules by IAU's Working Group for Planetary System Nomenclature, all new craters must be named after an artist that was famous for more than fifty years, and dead for more than three years, before the date they are named. Craters larger than 250 km in diameter are referred to as "basins" (also see ).
As of 2021, there are 414 named Mercurian craters, a small fraction of the total number of named Solar System craters, most of which are lunar, Martian and Venerian craters.
Other, non-planetary bodies with numerous named craters include Callisto (141), Ganymede (131), Rhea (128), Vesta (90), Ceres (90), Dione (73), Iapetus (58), Enceladus (53), Tethys (50) and Europa (41). For a full list, see List of craters in the Solar System.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
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R
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Terminology
As on the Moon and Mars, sequences of craters and basins of differing relative ages provide the best means of establishing stratigraphic order on Mercury. Overlap relations among many large mercurian craters and basins are clearer than those on the Moon. Therefore, as this map shows, we can build up many local stratigraphic columns involving both crater or basin materials and nearby plains materials.
Over all of Mercury, the crispness of crater rims and the morphology of their walls, central peaks, ejecta deposits, and secondary-crater fields have undergone systematic changes with time. The youngest craters or basins in a local stratigraphic sequence have the sharpest, crispest appearance. The oldest craters consist only of shallow depressions with slightly raised, rounded rims, some incomplete. On this basis, five age categories of craters and basins have been mapped; the characteristics of each are listed in the explanation. In addition, secondary crater fields are preserved around proportionally far more craters and basins on Mercury than on the Moon or Mars, and are particularly useful in determining overlap relations and degree of modification.
Because only limited photographic evidence was available from Mariner 10s three flybys of the planet, these divisions are often tentative. The five crater groups, from youngest to oldest, are:
c5: Fresh-appearing, sharp-rimmed, rayed craters. Highest albedo in map area; haloes and rays may extend many crater diameters from rim crests. Superposed on all other map units. Generally smaller and fewer than older craters.
c4: Fresh but slightly modified craters—Similar in morphology to c5 craters but without bright haloes or rays; sharp rim crests; continuous ejecta blankets; very few superposed secondary craters. Floors consist of crater or smooth plains materials.
c3: Modified craters—Rim crest continuous but slightly rounded and subdued. Ejecta blanket generally less extensive than those of younger craters of similar size. Superposed craters and rays common; smooth plains and intermediate plains materials cover floors of many craters. Central peaks more common than in c4 craters, probably because of larger average size of c3 craters.
c2: Subdued craters—Low-rimmed, relatively shallow craters, many with discontinuous rim crests. Floors covered by smooth plains and intermediate plains materials. Crater density of ejecta blankets similar to that of intermediate plains material.
c1 Degraded craters—Similar to c2 crater material but more deteriorated; many superposed craters.
See also
List of geological features on Mercury
List of quadrangles on Mercury
Note
References
Batson R.M., Russell J.F. (1994), Gazetteer of Planetary Nomenclature, United States Geological Survey Bulletin 2129
Davies M.E., Dwornik S.E., Gault D.E., Strom R.G. (1978), Atlas of Mercury, NASA Scientific and Technical Information Office
External links
USGS: Mercury nomenclature
USGS: Mercury Nomenclature: Craters
Atlas of Mercury
Mercury
Mercury (planet)-related lists
sv:Lista över geologiska strukturer på Merkurius#Kratrar | List of craters on Mercury | [
"Astronomy"
] | 908 | [
"Astronomy-related lists",
"Lists of impact craters"
] |
363,325 | https://en.wikipedia.org/wiki/Homogeneous%20space | In mathematics, a homogeneous space is, very informally, a space that looks the same everywhere, as you move through it, with movement given by the action of a group. Homogeneous spaces occur in the theories of Lie groups, algebraic groups and topological groups. More precisely, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts transitively. The elements of G are called the symmetries of X. A special case of this is when the group G in question is the automorphism group of the space X – here "automorphism group" can mean isometry group, diffeomorphism group, or homeomorphism group. In this case, X is homogeneous if intuitively X looks locally the same at each point, either in the sense of isometry (rigid geometry), diffeomorphism (differential geometry), or homeomorphism (topology). Some authors insist that the action of G be faithful (non-identity elements act non-trivially), although the present article does not. Thus there is a group action of G on X that can be thought of as preserving some "geometric structure" on X, and making X into a single G-orbit.
Formal definition
Let X be a non-empty set and G a group. Then X is called a G-space if it is equipped with an action of G on X. Note that automatically G acts by automorphisms (bijections) on the set. If X in addition belongs to some category, then the elements of G are assumed to act as automorphisms in the same category. That is, the maps on X coming from elements of G preserve the structure associated with the category (for example, if X is an object in Diff then the action is required to be by diffeomorphisms). A homogeneous space is a G-space on which G acts transitively.
If X is an object of the category C, then the structure of a G-space is a homomorphism:
into the group of automorphisms of the object X in the category C. The pair defines a homogeneous space provided ρ(G) is a transitive group of symmetries of the underlying set of X.
Examples
For example, if X is a topological space, then group elements are assumed to act as homeomorphisms on X. The structure of a G-space is a group homomorphism ρ : G → Homeo(X) into the homeomorphism group of X.
Similarly, if X is a differentiable manifold, then the group elements are diffeomorphisms. The structure of a G-space is a group homomorphism into the diffeomorphism group of X.
Riemannian symmetric spaces are an important class of homogeneous spaces, and include many of the examples listed below.
Concrete examples include:
Isometry groups
Positive curvature:
Sphere (orthogonal group): . This is true because of the following observations: First, Sn−1 is the set of vectors in Rn with norm 1. If we consider one of these vectors as a base vector, then any other vector can be constructed using an orthogonal transformation. If we consider the span of this vector as a one dimensional subspace of Rn, then the complement is an -dimensional vector space that is invariant under an orthogonal transformation from . This shows us why we can construct Sn−1 as a homogeneous space.
Oriented sphere (special orthogonal group):
Projective space (projective orthogonal group):
Flat (zero curvature):
Euclidean space (Euclidean group, point stabilizer is orthogonal group):
Negative curvature:
Hyperbolic space (orthochronous Lorentz group, point stabilizer orthogonal group, corresponding to hyperboloid model):
Oriented hyperbolic space:
Anti-de Sitter space:
Others
Affine space over field K (for affine group, point stabilizer general linear group): .
Grassmannian:
Topological vector spaces (in the sense of topology)
There are other interesting homogeneous spaces, in particular with relevance in physics: This includes Minkowski space or Galilean and Carrollian spaces.
Geometry
From the point of view of the Erlangen program, one may understand that "all points are the same", in the geometry of X. This was true of essentially all geometries proposed before Riemannian geometry, in the middle of the nineteenth century.
Thus, for example, Euclidean space, affine space and projective space are all in natural ways homogeneous spaces for their respective symmetry groups. The same is true of the models found of non-Euclidean geometry of constant curvature, such as hyperbolic space.
A further classical example is the space of lines in projective space of three dimensions (equivalently, the space of two-dimensional subspaces of a four-dimensional vector space). It is simple linear algebra to show that GL4 acts transitively on those. We can parameterize them by line co-ordinates: these are the 2×2 minors of the 4×2 matrix with columns two basis vectors for the subspace. The geometry of the resulting homogeneous space is the line geometry of Julius Plücker.
Homogeneous spaces as coset spaces
In general, if X is a homogeneous space of G, and Ho is the stabilizer of some marked point o in X (a choice of origin), the points of X correspond to the left cosets G/Ho, and the marked point o corresponds to the coset of the identity. Conversely, given a coset space G/H, it is a homogeneous space for G with a distinguished point, namely the coset of the identity. Thus a homogeneous space can be thought of as a coset space without a choice of origin.
For example, if H is the identity subgroup , then X is the G-torsor, which explains why G-torsors are often described intuitively as "G with forgotten identity".
In general, a different choice of origin o will lead to a quotient of G by a different subgroup Ho′ that is related to Ho by an inner automorphism of G. Specifically,
where g is any element of G for which . Note that the inner automorphism (1) does not depend on which such g is selected; it depends only on g modulo Ho.
If the action of G on X is continuous and X is Hausdorff, then H is a closed subgroup of G. In particular, if G is a Lie group, then H is a Lie subgroup by Cartan's theorem. Hence is a smooth manifold and so X carries a unique smooth structure compatible with the group action.
One can go further to double coset spaces, notably Clifford–Klein forms Γ\G/H, where Γ is a discrete subgroup (of G) acting properly discontinuously.
Example
For example, in the line geometry case, we can identify H as a 12-dimensional subgroup of the 16-dimensional general linear group, GL(4), defined by conditions on the matrix entries
h13 = h14 = h23 = h24 = 0,
by looking for the stabilizer of the subspace spanned by the first two standard basis vectors. That shows that X has dimension 4.
Since the homogeneous coordinates given by the minors are 6 in number, this means that the latter are not independent of each other. In fact, a single quadratic relation holds between the six minors, as was known to nineteenth-century geometers.
This example was the first known example of a Grassmannian, other than a projective space. There are many further homogeneous spaces of the classical linear groups in common use in mathematics.
Prehomogeneous vector spaces
The idea of a prehomogeneous vector space was introduced by Mikio Sato.
It is a finite-dimensional vector space V with a group action of an algebraic group G, such that there is an orbit of G that is open for the Zariski topology (and so, dense). An example is GL(1) acting on a one-dimensional space.
The definition is more restrictive than it initially appears: such spaces have remarkable properties, and there is a classification of irreducible prehomogeneous vector spaces, up to a transformation known as "castling".
Homogeneous spaces in physics
Given the Poincaré group G and its subgroup the Lorentz group H, the space of cosets is the Minkowski space. Together with de Sitter space and Anti-de Sitter space these are the maximally symmetric lorentzian spacetimes. There are also homogeneous spaces of relevance in physics that are non-lorentzian, for example Galilean, Carrollian or Aristotelian spacetimes.
Physical cosmology using the general theory of relativity makes use of the Bianchi classification system. Homogeneous spaces in relativity represent the space part of background metrics for some cosmological models; for example, the three cases of the Friedmann–Lemaître–Robertson–Walker metric may be represented by subsets of the Bianchi I (flat), V (open), VII (flat or open) and IX (closed) types, while the Mixmaster universe represents an anisotropic example of a Bianchi IX cosmology.
A homogeneous space of N dimensions admits a set of Killing vectors. For three dimensions, this gives a total of six linearly independent Killing vector fields; homogeneous 3-spaces have the property that one may use linear combinations of these to find three everywhere non-vanishing Killing vector fields ξ,
where the object Cabc, the "structure constants", form a constant order-three tensor antisymmetric in its lower two indices (on the left-hand side, the brackets denote antisymmetrisation and ";" represents the covariant differential operator). In the case of a flat isotropic universe, one possibility is (type I), but in the case of a closed FLRW universe, , where εabcis the Levi-Civita symbol.
See also
Erlangen program
Klein geometry
Heap (mathematics)
Homogeneous variety
Notes
References
John Milnor & James D. Stasheff (1974) Characteristic Classes, Princeton University Press
Takashi Koda An Introduction to the Geometry of Homogeneous Spaces from Kyungpook National University
Menelaos Zikidis Homogeneous Spaces from Heidelberg University
Shoshichi Kobayashi, Katsumi Nomizu (1969) Foundations of Differential Geometry, volume 2, chapter X, (Wiley Classics Library)
Topological groups
Lie groups | Homogeneous space | [
"Physics",
"Mathematics"
] | 2,157 | [
"Lie groups",
"Mathematical structures",
"Group actions",
"Homogeneous spaces",
"Space (mathematics)",
"Topological spaces",
"Algebraic structures",
"Geometry",
"Topological groups",
"Symmetry"
] |
363,360 | https://en.wikipedia.org/wiki/Lyapunov%20stability | Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis). The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.
History
Lyapunov stability is named after Aleksandr Mikhailovich Lyapunov, a Russian mathematician who defended the thesis The General Problem of Stability of Motion at Kharkov University in 1892. A. M. Lyapunov was a pioneer in successful endeavors to develop a global approach to the analysis of the stability of nonlinear dynamical systems by comparison with the widely spread local method of linearizing them about points of equilibrium. His work, initially published in Russian and then translated to French, received little attention for many years. The mathematical theory of stability of motion, founded by A. M. Lyapunov, considerably anticipated the time for its implementation in science and technology. Moreover Lyapunov did not himself make application in this field, his own interest being in the stability of rotating fluid masses with astronomical application. He did not have doctoral students who followed the research in the field of stability and his own destiny was terribly tragic because of his suicide in 1918 . For several decades the theory of stability sank into complete oblivion. The Russian-Soviet mathematician and mechanician Nikolay Gur'yevich Chetaev working at the Kazan Aviation Institute in the 1930s was the first who realized the incredible magnitude of the discovery made by A. M. Lyapunov. The contribution to the theory made by N. G. Chetaev was so significant that many mathematicians, physicists and engineers consider him Lyapunov's direct successor and the next-in-line scientific descendant in the creation and development of the mathematical theory of stability.
The interest in it suddenly skyrocketed during the Cold War period when the so-called "Second Method of Lyapunov" (see below) was found to be applicable to the stability of aerospace guidance systems which typically contain strong nonlinearities not treatable by other methods. A large number of publications appeared then and since in the control and systems literature.
More recently the concept of the Lyapunov exponent (related to Lyapunov's First Method of discussing stability) has received wide interest in connection with chaos theory. Lyapunov stability methods have also been applied to finding equilibrium solutions in traffic assignment problems.
Definition for continuous-time systems
Consider an autonomous nonlinear dynamical system
,
where denotes the system state vector, an open set containing the origin, and is a continuous vector field on . Suppose has an equilibrium at so that then
This equilibrium is said to be Lyapunov stable if for every there exists a such that if then for every we have .
The equilibrium of the above system is said to be asymptotically stable if it is Lyapunov stable and there exists such that if then .
The equilibrium of the above system is said to be exponentially stable if it is asymptotically stable and there exist such that if then for all .
Conceptually, the meanings of the above terms are the following:
Lyapunov stability of an equilibrium means that solutions starting "close enough" to the equilibrium (within a distance from it) remain "close enough" forever (within a distance from it). Note that this must be true for any that one may want to choose.
Asymptotic stability means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium.
Exponential stability means that solutions not only converge, but in fact converge faster than or at least as fast as a particular known rate .
The trajectory is (locally) attractive if
as
for all trajectories that start close enough to , and globally attractive if this property holds for all trajectories.
That is, if x belongs to the interior of its stable manifold, it is asymptotically stable if it is both attractive and stable. (There are examples showing that attractivity does not imply asymptotic stability. Such examples are easy to create using homoclinic connections.)
If the Jacobian of the dynamical system at an equilibrium happens to be a stability matrix (i.e., if the real part of each eigenvalue is strictly negative), then the equilibrium is asymptotically stable.
System of deviations
Instead of considering stability only near an equilibrium point (a constant solution ), one can formulate similar definitions of stability near an arbitrary solution . However, one can reduce the more general case to that of an equilibrium by a change of variables called a "system of deviations". Define , obeying the differential equation:
.
This is no longer an autonomous system, but it has a guaranteed equilibrium point at whose stability is equivalent to the stability of the original solution .
Lyapunov's second method for stability
Lyapunov, in his original 1892 work, proposed two methods for demonstrating stability. The first method developed the solution in a series which was then proved convergent within limits. The second method, which is now referred to as the Lyapunov stability criterion or the Direct Method, makes use of a Lyapunov function V(x) which has an analogy to the potential function of classical dynamics. It is introduced as follows for a system having a point of equilibrium at . Consider a function such that
if and only if
if and only if
for all values of . Note: for asymptotic stability, for is required.
Then V(x) is called a Lyapunov function and the system is stable in the sense of Lyapunov. (Note that is required; otherwise for example would "prove" that is locally stable.) An additional condition called "properness" or "radial unboundedness" is required in order to conclude global stability. Global asymptotic stability (GAS) follows similarly.
It is easier to visualize this method of analysis by thinking of a physical system (e.g. vibrating spring and mass) and considering the energy of such a system. If the system loses energy over time and the energy is never restored then eventually the system must grind to a stop and reach some final resting state. This final state is called the attractor. However, finding a function that gives the precise energy of a physical system can be difficult, and for abstract mathematical systems, economic systems or biological systems, the concept of energy may not be applicable.
Lyapunov's realization was that stability can be proven without requiring knowledge of the true physical energy, provided a Lyapunov function can be found to satisfy the above constraints.
Definition for discrete-time systems
The definition for discrete-time systems is almost identical to that for continuous-time systems. The definition below provides this, using an alternate language commonly used in more mathematical texts.
Let (X, d) be a metric space and f : X → X a continuous function. A point x in X is said to be Lyapunov stable, if,
We say that x is asymptotically stable if it belongs to the interior of its stable set, i.e. if,
Stability for linear state space models
A linear state space model
,
where is a finite matrix, is asymptotically stable (in fact, exponentially stable) if all real parts of the eigenvalues of are negative. This condition is equivalent to the following one:
is negative definite for some positive definite matrix . (The relevant Lyapunov function is .)
Correspondingly, a time-discrete linear state space model
is asymptotically stable (in fact, exponentially stable) if all the eigenvalues of have a modulus smaller than one.
This latter condition has been generalized to switched systems: a linear switched discrete time system (ruled by a set of matrices )
is asymptotically stable (in fact, exponentially stable) if the joint spectral radius of the set is smaller than one.
Stability for systems with inputs
A system with inputs (or controls) has the form
where the (generally time-dependent) input u(t) may be viewed as a control, external input,
stimulus, disturbance, or forcing function. It has been shown that near to a point of equilibrium which is Lyapunov stable the system remains stable under small disturbances. For larger input disturbances the study of such systems is the subject of control theory and applied in control engineering. For systems with inputs, one must quantify the effect of inputs on the stability of the system. The main two approaches to this analysis are BIBO stability (for linear systems) and input-to-state stability (ISS) (for nonlinear systems)
Example
This example shows a system where a Lyapunov function can be used to prove Lyapunov stability but cannot show asymptotic stability.
Consider the following equation, based on the Van der Pol oscillator equation with the friction term changed:
Let
so that the corresponding system is
The origin is the only equilibrium point.
Let us choose as a Lyapunov function
which is clearly positive definite. Its derivative is
It seems that if the parameter is positive, stability is asymptotic for But this is wrong, since does not depend on , and will be 0 everywhere on the axis. The equilibrium is Lyapunov stable but not asymptotically stable.
Barbalat's lemma and stability of time-varying systems
It may be difficult to find a Lyapunov function with a negative definite derivative as required by the Lyapunov stability criterion, however a function with that is only negative semi-definite may be available. In autonomous systems, the invariant set theorem can be applied to prove asymptotic stability, but this theorem is not applicable when the dynamics are a function of time.
Instead, Barbalat's lemma allows for Lyapunov-like analysis of these non-autonomous systems. The lemma is motivated by the following observations. Assuming f is a function of time only:
Having does not imply that has a limit at . For example, .
Having approaching a limit as does not imply that . For example, .
Having lower bounded and decreasing () implies it converges to a limit. But it does not say whether or not as .
Barbalat's Lemma says:
If has a finite limit as and if is uniformly continuous (a sufficient condition for uniform continuity is that is bounded), then as .
An alternative version is as follows:
Let and . If and , then as
In the following form the Lemma is true also in the vector valued case:
Let be a uniformly continuous function with values in a Banach space and assume that has a finite limit as . Then as .
The following example is taken from page 125 of Slotine and Li's book Applied Nonlinear Control.
Consider a non-autonomous system
This is non-autonomous because the input is a function of time. Assume that the input is bounded.
Taking gives
This says that by first two conditions and hence and are bounded. But it does not say anything about the convergence of to zero, as is only negative semi-definite (note can be non-zero when =0) and the dynamics are non-autonomous.
Using Barbalat's lemma:
.
This is bounded because , and are bounded. This implies as and hence . This proves that the error converges.
See also
Lyapunov function
LaSalle's invariance principle
Lyapunov–Malkin theorem
Markus–Yamabe conjecture
Libration point orbit
Hartman–Grobman theorem
Perturbation theory
References
Further reading
Stability theory
Dynamical systems
Lagrangian mechanics
Three-body orbits | Lyapunov stability | [
"Physics",
"Mathematics"
] | 2,553 | [
"Lagrangian mechanics",
"Classical mechanics",
"Stability theory",
"Mechanics",
"Dynamical systems"
] |
363,377 | https://en.wikipedia.org/wiki/Fredholm%20integral%20equation | In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. A useful method to solve such equations, the Adomian decomposition method, is due to George Adomian.
Equation of the first kind
A Fredholm equation is an integral equation in which the term containing the kernel function (defined below) has constants as integration limits. A closely related form is the Volterra integral equation which has variable integral limits.
An inhomogeneous Fredholm equation of the first kind is written as
and the problem is, given the continuous kernel function and the function , to find the function .
An important case of these types of equation is the case when the kernel is a function only of the difference of its arguments, namely , and the limits of integration are ±∞, then the right hand side of the equation can be rewritten as a convolution of the functions and and therefore, formally, the solution is given by
where and are the direct and inverse Fourier transforms, respectively. This case would not be typically included under the umbrella of Fredholm integral equations, a name that is usually reserved for when the integral operator defines a compact operator (convolution operators on non-compact groups are non-compact, since, in general, the spectrum of the operator of convolution with contains the range of , which is usually a non-countable set, whereas compact operators have discrete countable spectra).
Equation of the second kind
An inhomogeneous Fredholm equation of the second kind is given as
Given the kernel , and the function , the problem is typically to find the function .
A standard approach to solving this is to use iteration, amounting to the resolvent formalism; written as a series, the solution is known as the Liouville–Neumann series.
General theory
The general theory underlying the Fredholm equations is known as Fredholm theory. One of the principal results is that the kernel yields a compact operator. Compactness may be shown by invoking equicontinuity. As an operator, it has a spectral theory that can be understood in terms of a discrete spectrum of eigenvalues that tend to 0.
Applications
Fredholm equations arise naturally in the theory of signal processing, for example as the famous spectral concentration problem popularized by David Slepian. The operators involved are the same as linear filters. They also commonly arise in linear forward modeling and inverse problems. In physics, the solution of such integral equations allows for experimental spectra to be related to various underlying distributions, for instance the mass distribution of polymers in a polymeric melt,
or the distribution of relaxation times in the system.
In addition, Fredholm integral equations also arise in fluid mechanics problems involving hydrodynamic interactions near finite-sized elastic interfaces.
A specific application of Fredholm equation is the generation of photo-realistic images in computer graphics, in which the Fredholm equation is used to model light transport from the virtual light sources to the image plane. The Fredholm equation is often called the rendering equation in this context.
See also
Liouville–Neumann series
Volterra integral equation
Fredholm alternative
References
Further reading
Integral Equations at EqWorld: The World of Mathematical Equations.
A.D. Polyanin and A.V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton, 1998.
Mathews, Jon; Walker, Robert L. (1970), Mathematical methods of physics (2nd ed.), New York: W. A. Benjamin,
External links
IntEQ: a Python package for numerically solving Fredholm integral equations
Fredholm theory
Integral equations | Fredholm integral equation | [
"Mathematics"
] | 761 | [
"Mathematical objects",
"Integral equations",
"Equations"
] |
363,400 | https://en.wikipedia.org/wiki/Combinatorial%20topology | In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour.
The change of name reflected the move to organise topological classes such as cycles-modulo-boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence. The transition is also attributed to the work of Heinz Hopf, who was influenced by Noether, and to Leopold Vietoris and Walther Mayer, who independently defined homology.
A fairly precise date can be supplied in the internal notes of the Bourbaki group. While topology was still combinatorial in 1942, it had become algebraic by 1944. This corresponds also to the period where homological algebra and category theory were introduced for the study of topological spaces, and largely supplanted combinatorial methods.
Azriel Rosenfeld (1973) proposed digital topology for a type of image processing that can be considered as a new development of combinatorial topology. The digital forms of the Euler characteristic theorem and the Gauss–Bonnet theorem were obtained by Li Chen and Yongwu Rong. A 2D grid cell topology already appeared in the Alexandrov–Hopf book Topologie I (1935).
See also
Hauptvermutung
Topological combinatorics
Topological graph theory
Notes
References
Algebraic topology
Combinatorics
es:Topología combinatoria | Combinatorial topology | [
"Mathematics"
] | 341 | [
"Discrete mathematics",
"Algebraic topology",
"Combinatorics",
"Fields of abstract algebra",
"Topology"
] |
363,430 | https://en.wikipedia.org/wiki/Photochemistry | Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet (wavelength from 100 to 400 nm), visible (400–750 nm), or infrared radiation (750–2500 nm).
In nature, photochemistry is of immense importance as it is the basis of photosynthesis, vision, and the formation of vitamin D with sunlight. It is also responsible for the appearance of DNA mutations leading to skin cancers.
Photochemical reactions proceed differently than temperature-driven reactions. Photochemical paths access high-energy intermediates that cannot be generated thermally, thereby overcoming large activation barriers in a short period of time, and allowing reactions otherwise inaccessible by thermal processes. Photochemistry can also be destructive, as illustrated by the photodegradation of plastics.
Concept
Grotthuss–Draper law and Stark–Einstein law
Photoexcitation is the first step in a photochemical process where the reactant is elevated to a state of higher energy, an excited state. The first law of photochemistry, known as the Grotthuss–Draper law (for chemists Theodor Grotthuss and John W. Draper), states that light must be absorbed by a chemical substance in order for a photochemical reaction to take place. According to the second law of photochemistry, known as the Stark–Einstein law (for physicists Johannes Stark and Albert Einstein), for each photon of light absorbed by a chemical system, no more than one molecule is activated for a photochemical reaction, as defined by the quantum yield.
Fluorescence and phosphorescence
When a molecule or atom in the ground state (S0) absorbs light, one electron is excited to a higher orbital level. This electron maintains its spin according to the spin selection rule; other transitions would violate the law of conservation of angular momentum. The excitation to a higher singlet state can be from HOMO to LUMO or to a higher orbital, so that singlet excitation states S1, S2, S3... at different energies are possible.
Kasha's rule stipulates that higher singlet states would quickly relax by radiationless decay or internal conversion (IC) to S1. Thus, S1 is usually, but not always, the only relevant singlet excited state. This excited state S1 can further relax to S0 by IC, but also by an allowed radiative transition from S1 to S0 that emits a photon; this process is called fluorescence.
Alternatively, it is possible for the excited state S1 to undergo spin inversion and to generate a triplet excited state T1 having two unpaired electrons with the same spin. This violation of the spin selection rule is possible by intersystem crossing (ISC) of the vibrational and electronic levels of S1 and T1. According to Hund's rule of maximum multiplicity, this T1 state would be somewhat more stable than S1.
This triplet state can relax to the ground state S0 by radiationless ISC or by a radiation pathway called phosphorescence. This process implies a change of electronic spin, which is forbidden by spin selection rules, making phosphorescence (from T1 to S0) much slower than fluorescence (from S1 to S0). Thus, triplet states generally have longer lifetimes than singlet states. These transitions are usually summarized in a state energy diagram or Jablonski diagram, the paradigm of molecular photochemistry.
These excited species, either S1 or T1, have a half-empty low-energy orbital, and are consequently more oxidizing than the ground state. But at the same time, they have an electron in a high-energy orbital, and are thus more reducing. In general, excited species are prone to participate in electron transfer processes.
Experimental setup
Photochemical reactions require a light source that emits wavelengths corresponding to an electronic transition in the reactant. In the early experiments (and in everyday life), sunlight was the light source, although it is polychromatic. Mercury-vapor lamps are more common in the laboratory. Low-pressure mercury-vapor lamps mainly emit at 254 nm. For polychromatic sources, wavelength ranges can be selected using filters. Alternatively, laser beams are usually monochromatic (although two or more wavelengths can be obtained using nonlinear optics), and LEDs have a relatively narrow band that can be efficiently used, as well as Rayonet lamps, to get approximately monochromatic beams.
The emitted light must reach the targeted functional group without being blocked by the reactor, medium, or other functional groups present. For many applications, quartz is used for the reactors as well as to contain the lamp. Pyrex absorbs at wavelengths shorter than 275 nm. The solvent is an important experimental parameter. Solvents are potential reactants, and for this reason, chlorinated solvents are avoided because the C–Cl bond can lead to chlorination of the substrate. Strongly-absorbing solvents prevent photons from reaching the substrate. Hydrocarbon solvents absorb only at short wavelengths and are thus preferred for photochemical experiments requiring high-energy photons. Solvents containing unsaturation absorb at longer wavelengths and can usefully filter out short wavelengths. For example, cyclohexane and acetone "cut off" (absorb strongly) at wavelengths shorter than 215 and 330 nm, respectively.
Typically, the wavelength employed to induce a photochemical process is selected based on the absorption spectrum of the reactive species, most often the absorption maximum. Over the last years, however, it has been demonstrated that, in the majority of bond-forming reactions, the absorption spectrum does not allow selecting the optimum wavelength to achieve the highest reaction yield based on absorptivity. This fundamental mismatch between absorptivity and reactivity has been elucidated with so-called photochemical action plots.
Photochemistry in combination with flow chemistry
Continuous-flow photochemistry offers multiple advantages over batch photochemistry. Photochemical reactions are driven by the number of photons that are able to activate molecules causing the desired reaction. The large surface-area-to-volume ratio of a microreactor maximizes the illumination, and at the same time allows for efficient cooling, which decreases the thermal side products.
Principles
In the case of photochemical reactions, light provides the activation energy. Simplistically, light is one mechanism for providing the activation energy required for many reactions. If laser light is employed, it is possible to selectively excite a molecule so as to produce a desired electronic and vibrational state. Equally, the emission from a particular state may be selectively monitored, providing a measure of the population of that state. If the chemical system is at low pressure, this enables scientists to observe the energy distribution of the products of a chemical reaction before the differences in energy have been smeared out and averaged by repeated collisions.
The absorption of a photon by a reactant molecule may also permit a reaction to occur not just by bringing the molecule to the necessary activation energy, but also by changing the symmetry of the molecule's electronic configuration, enabling an otherwise-inaccessible reaction path, as described by the Woodward–Hoffmann selection rules. A [2+2] cycloaddition reaction is one example of a pericyclic reaction that can be analyzed using these rules or by the related frontier molecular orbital theory.
Some photochemical reactions are several orders of magnitude faster than thermal reactions; reactions as fast as 10−9 seconds and associated processes as fast as 10−15 seconds are often observed.
The photon can be absorbed directly by the reactant or by a photosensitizer, which absorbs the photon and transfers the energy to the reactant. The opposite process, when a photoexcited state is deactivated by a chemical reagent, is called quenching.
Most photochemical transformations occur through a series of simple steps known as primary photochemical processes. One common example of these processes is the excited state proton transfer.
Photochemical reactions
Examples of photochemical reactions
Photosynthesis: Plants use solar energy to convert carbon dioxide and water into glucose and oxygen.
Human formation of vitamin D by exposure to sunlight.
Bioluminescence: e.g. In fireflies, an enzyme in the abdomen catalyzes a reaction that produces light.
Polymerizations started by photoinitiators, which decompose upon absorbing light to produce the free radicals for radical polymerization.
Photodegradation of many substances, e.g. polyvinyl chloride and Fp. Medicine bottles are often made from darkened glass to protect the drugs from photodegradation.
Photochemical rearrangements, e.g. photoisomerization, hydrogen atom transfer, and photochemical electrocyclic reactions.
Photodynamic therapy: Light is used to destroy tumors by the action of singlet oxygen generated by photosensitized reactions of triplet oxygen. Typical photosensitizers include tetraphenylporphyrin and methylene blue. The resulting singlet oxygen is an aggressive oxidant, capable of converting C–H bonds into C–OH groups.
Diazo printing process
Photoresist technology, used in the production of microelectronic components.
Vision is initiated by a photochemical reaction of rhodopsin.
Toray photochemical production of ε-caprolactame.
Photochemical production of artemisinin, an anti-malaria drug.
Photoalkylation, used for the light-induced addition of alkyl groups to molecules.
DNA: photodimerization leading to cyclobutane pyrimidine dimers.
Organic photochemistry
Examples of photochemical organic reactions are electrocyclic reactions, radical reactions, photoisomerization, and Norrish reactions.
Alkenes undergo many important reactions that proceed via a photon-induced π to π* transition. The first electronic excited state of an alkene lacks the π-bond, so that rotation about the C–C bond is rapid and the molecule engages in reactions not observed thermally. These reactions include cis-trans isomerization and cycloaddition to other (ground state) alkene to give cyclobutane derivatives. The cis-trans isomerization of a (poly)alkene is involved in retinal, a component of the machinery of vision. The dimerization of alkenes is relevant to the photodamage of DNA, where thymine dimers are observed upon illuminating DNA with UV radiation. Such dimers interfere with transcription. The beneficial effects of sunlight are associated with the photochemically-induced retro-cyclization (decyclization) reaction of ergosterol to give vitamin D. In the DeMayo reaction, an alkene reacts with a 1,3-diketone reacts via its enol to yield a 1,5-diketone. Still another common photochemical reaction is Howard Zimmerman's di-π-methane rearrangement.
In an industrial application, about 100,000 tonnes of benzyl chloride are prepared annually by the gas-phase photochemical reaction of toluene with chlorine. The light is absorbed by chlorine molecules, the low energy of this transition being indicated by the yellowish color of the gas. The photon induces homolysis of the Cl-Cl bond, and the resulting chlorine radical converts toluene to the benzyl radical:
Cl2 + hν → 2 Cl·
C6H5CH3 + Cl· → C6H5CH2· + HCl
C6H5CH2· + Cl· → C6H5CH2Cl
Mercaptans can be produced by photochemical addition of hydrogen sulfide (H2S) to alpha olefins.
Inorganic and organometallic photochemistry
Coordination complexes and organometallic compounds are also photoreactive. These reactions can entail cis-trans isomerization. More commonly, photoreactions result in dissociation of ligands, since the photon excites an electron on the metal to an orbital that is antibonding with respect to the ligands. Thus, metal carbonyls that resist thermal substitution undergo decarbonylation upon irradiation with UV light. UV-irradiation of a THF solution of molybdenum hexacarbonyl gives the THF complex, which is synthetically useful:
Mo(CO)6 + THF → Mo(CO)5(THF) + CO
In a related reaction, photolysis of iron pentacarbonyl affords diiron nonacarbonyl (see figure):
2 Fe(CO)5 → Fe2(CO)9 + CO
Select photoreactive coordination complexes can undergo oxidation-reduction processes via single electron transfer. This electron transfer can occur within the inner or outer coordination sphere of the metal.
Types of photochemical reactions
Here are some different types of photochemical reactions-
Photo-dissociation: AB + hν → A* + B*
Photo induced rearrangements, isomerization: A + hν → B
Photo-addition: A + B + hν → AB + C
Photo-substitution: A + BC + hν → AB + C
Photo-redox reaction: A + B + hν → A− + B+
Historical
Although bleaching has long been practiced, the first photochemical reaction was described by Trommsdorff in 1834. He observed that crystals of the compound α-santonin when exposed to sunlight turned yellow and burst. In a 2007 study the reaction was described as a succession of three steps taking place within a single crystal.
The first step is a rearrangement reaction to a cyclopentadienone intermediate (2), the second one a dimerization in a Diels–Alder reaction (3), and the third one an intramolecular [2+2]cycloaddition (4). The bursting effect is attributed to a large change in crystal volume on dimerization.
Specialized journals
Journal of Photochemistry and Photobiology
ChemPhotoChem
Photochemistry and Photobiology
Photochemical & Photobiological Sciences
Photochemistry
Learned societies
Inter-American Photochemical Society
European Photochemistry Association
Asian and Oceanian Photochemistry Association
International conferences
IUPAC SYmposium on Photochemistry (biennial)
International Conference on Photochemitry (biennial)
The organization of these conferences is facilitated by the International Foundation for Photochemistry.
See also
Photonic molecule
Photoelectrochemical cell
Photochemical logic gate
Photosynthesis
Light-dependent reactions
List of photochemists
Single photon sources
Photogeochemistry
Photoelectric effect
Photolysis
Blueprint
References
Further reading
Bowen, E. J., Chemical Aspects of Light. Oxford: The Clarendon Press, 1942. 2nd edition, 1946.
Photochemistry
Chemistry | Photochemistry | [
"Chemistry"
] | 3,074 | [
"nan"
] |
363,441 | https://en.wikipedia.org/wiki/Principal%20homogeneous%20space | In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively (meaning that, for any x, y in X, there exists a unique g in G such that , where · denotes the (right) action of G on X).
An analogous definition holds in other categories, where, for example,
G is a topological group, X is a topological space and the action is continuous,
G is a Lie group, X is a smooth manifold and the action is smooth,
G is an algebraic group, X is an algebraic variety and the action is regular.
Definition
If G is nonabelian then one must distinguish between left and right torsors according to whether the action is on the left or right. In this article, we will use right actions.
To state the definition more explicitly, X is a G-torsor or G-principal homogeneous space if X is nonempty and is equipped with a map (in the appropriate category) such that
x·1 = x
x·(gh) = (x·g)·h
for all and all , and such that the map given by
is an isomorphism (of sets, or topological spaces or ..., as appropriate, i.e. in the category in question).
Note that this means that X and G are isomorphic (in the category in question; not as groups: see the following). However—and this is the essential point—there is no preferred 'identity' point in X. That is, X looks exactly like G except that which point is the identity has been forgotten. (This concept is often used in mathematics as a way of passing to a more intrinsic point of view, under the heading 'throw away the origin'.)
Since X is not a group, we cannot multiply elements; we can, however, take their "quotient". That is, there is a map that sends to the unique element such that .
The composition of the latter operation with the right group action, however, yields a ternary operation , which serves as an affine generalization of group multiplication and which is sufficient to both characterize a principal homogeneous space algebraically and intrinsically characterize the group it is associated with. If we denote the result of this ternary operation, then the following identities
will suffice to define a principal homogeneous space, while the additional property
identifies those spaces that are associated with abelian groups. The group may be defined as formal quotients subject to the equivalence relation
,
with the group product, identity and inverse defined, respectively, by
,
,
and the group action by
Examples
Every group G can itself be thought of as a left or right G-torsor under the natural action of left or right multiplication.
Another example is the affine space concept: the idea of the affine space A underlying a vector space V can be said succinctly by saying that A is a principal homogeneous space for V acting as the additive group of translations.
The flags of any regular polytope form a torsor for its symmetry group.
Given a vector space V we can take G to be the general linear group GL(V), and X to be the set of all (ordered) bases of V. Then G acts on X in the way that it acts on vectors of V; and it acts transitively since any basis can be transformed via G to any other. What is more, a linear transformation fixing each vector of a basis will fix all v in V, and hence be the neutral element of the general linear group GL(V) : so that X is indeed a principal homogeneous space. One way to follow basis-dependence in a linear algebra argument is to track variables x in X. Similarly, the space of orthonormal bases (the Stiefel manifold of n-frames) is a principal homogeneous space for the orthogonal group.
In category theory, if two objects X and Y are isomorphic, then the isomorphisms between them, Iso(X,Y), form a torsor for the automorphism group of X, Aut(X), and likewise for Aut(Y); a choice of isomorphism between the objects gives rise to an isomorphism between these groups and identifies the torsor with these two groups, giving the torsor a group structure (as it has now a base point).
Applications
The principal homogeneous space concept is a special case of that of principal bundle: it means a principal bundle with base a single point. In other words the local theory of principal bundles is that of a family of principal homogeneous spaces depending on some parameters in the base. The 'origin' can be supplied by a section of the bundle—such sections are usually assumed to exist locally on the base—the bundle being locally trivial, so that the local structure is that of a cartesian product. But sections will often not exist globally. For example a differential manifold M has a principal bundle of frames associated to its tangent bundle. A global section will exist (by definition) only when M is parallelizable, which implies strong topological restrictions.
In number theory there is a (superficially different) reason to consider principal homogeneous spaces, for elliptic curves E defined over a field K (and more general abelian varieties). Once this was understood, various other examples were collected under the heading, for other algebraic groups: quadratic forms for orthogonal groups, and Severi–Brauer varieties for projective linear groups being two.
The reason of the interest for Diophantine equations, in the elliptic curve case, is that K may not be algebraically closed. There can exist curves C that have no point defined over K, and which become isomorphic over a larger field to E, which by definition has a point over K to serve as identity element for its addition law. That is, for this case we should distinguish C that have genus 1, from elliptic curves E that have a K-point (or, in other words, provide a Diophantine equation that has a solution in K). The curves C turn out to be torsors over E, and form a set carrying a rich structure in the case that K is a number field (the theory of the Selmer group). In fact a typical plane cubic curve C over Q has no particular reason to have a rational point; the standard Weierstrass model always does, namely the point at infinity, but you need a point over K to put C into that form over K.
This theory has been developed with great attention to local analysis, leading to the definition of the Tate–Shafarevich group. In general the approach of taking the torsor theory, easy over an algebraically closed field, and trying to get back 'down' to a smaller field is an aspect of descent. It leads at once to questions of Galois cohomology, since the torsors represent classes in group cohomology H1.
Other usage
The concept of a principal homogeneous space can also be globalized as follows. Let X be a "space" (a scheme/manifold/topological space etc.), and let G be a group over X, i.e., a group object in the category of spaces over X. In this case, a (right, say) G-torsor E on X is a space E (of the same type) over X with a (right) G action such that the morphism
given by
is an isomorphism in the appropriate category, and such that E is locally trivial on X, in that acquires a section locally on X. Isomorphism classes of torsors in this sense correspond to classes in the cohomology group H1(X,G).
When we are in the smooth manifold category, then a G-torsor (for G a Lie group) is then precisely a principal G-bundle as defined above.
Example: if G is a compact Lie group (say), then is a G-torsor over the classifying space .
See also
Homogeneous space
Heap (mathematics)
Notes
Further reading
External links
Torsors made easy by John Baez
Group theory
Topological groups
Lie groups
Algebraic homogeneous spaces
Diophantine geometry
Vector bundles | Principal homogeneous space | [
"Mathematics"
] | 1,718 | [
"Lie groups",
"Mathematical structures",
"Space (mathematics)",
"Group theory",
"Topological spaces",
"Fields of abstract algebra",
"Algebraic structures",
"Topological groups"
] |
363,442 | https://en.wikipedia.org/wiki/Inorganic%20compound | An inorganic compound is typically a chemical compound that lacks carbon–hydrogen bondsthat is, a compound that is not an organic compound. The study of inorganic compounds is a subfield of chemistry known as inorganic chemistry.
Inorganic compounds comprise most of the Earth's crust, although the compositions of the deep mantle remain active areas of investigation.
All allotropes (structurally different pure forms of an element) and some simple carbon compounds are often considered inorganic. Examples include the allotropes of carbon (graphite, diamond, buckminsterfullerene, graphene, etc.), carbon monoxide , carbon dioxide , carbides, and salts of inorganic anions such as carbonates, cyanides, cyanates, thiocyanates, isothiocyanates, etc. Many of these are normal parts of mostly organic systems, including organisms; describing a chemical as inorganic does not necessarily mean that it cannot occur within living things.
History
Friedrich Wöhler's conversion of ammonium cyanate into urea in 1828 is often cited as the starting point of modern organic chemistry. In Wöhler's era, there was widespread belief that organic compounds were characterized by a vital spirit. In the absence of vitalism, the distinction between inorganic and organic chemistry is merely semantic.
Modern usage
The Inorganic Crystal Structure Database (ICSD) in its definition of "inorganic" carbon compounds, states that such compounds may contain either C-H or C-C bonds, but not both.
The book series Inorganic Syntheses does not define inorganic compounds. The majority of its content deals with metal complexes of organic ligands.
IUPAC does not offer a definition of "inorganic" or "inorganic compound" but does define inorganic polymer as "...skeletal structure that does not include carbon atoms."
See also
Inorganic compounds by element
List of inorganic compounds
List of named inorganic compounds
Mineral acid
References | Inorganic compound | [
"Chemistry"
] | 387 | [
"Inorganic compounds"
] |
363,445 | https://en.wikipedia.org/wiki/Dry%20cask%20storage | Dry cask storage is a method of storing high-level radioactive waste, such as spent nuclear fuel that has already been cooled in a spent fuel pool for at least one year and often as much as ten years. Casks are typically steel cylinders that are either welded or bolted closed. The fuel rods inside are surrounded by inert gas. Ideally, the steel cylinder provides leak-tight containment of the spent fuel. Each cylinder is surrounded by additional steel, concrete, or other material to provide radiation shielding to workers and members of the public.
There are various dry storage cask system designs. With some designs, the steel cylinders containing the fuel are placed vertically in a concrete vault; other designs orient the cylinders horizontally. The concrete vaults provide the radiation shielding. Other cask designs orient the steel cylinder vertically on a concrete pad at a dry cask storage site and use both metal and concrete outer cylinders for radiation shielding. Until 2024/25, there was no long term permanent storage facility anywhere in the world, and most countries still don't have a facility; dry cask storage is designed as an interim safer solution than spent fuel pool storage.
Some of the cask designs can be used for both storage and transportation. Three companies – Holtec International, NAC International and Areva-Transnuclear NUHOMS – are marketing Independent Spent Fuel Storage Installations (ISFSI) based upon an unshielded multi-purpose canister which is transported and stored in on-site vertical or horizontal shielded storage modules constructed of steel and concrete.
Usage
During the 2000s, dry cask storage was used in the United States, Canada, Germany, Switzerland, Spain, Belgium, the United Kingdom, Japan, Armenia, Argentina, Bulgaria, Czech Republic, Hungary, South Korea, Romania, Slovakia, Ukraine and Lithuania.
A similar system is also being implemented in Russia. However, it is based on 'storage compartments' in a single structure, rather than individual casks.
In 2017, France's Areva introduced the NUHOMS Matrix advanced used nuclear fuel storage overpack, a high-density system for storing multiple spent fuel rods in canisters.
United States
In the late 1970s and early 1980s, the need for alternative storage in the United States began to grow when cooling pools at many nuclear reactors began to fill with stored spent fuel. As there was not a national nuclear storage facility in operation at the time, utilities began looking at options for storing spent fuel. Dry cask storage was determined to be a practical option for storage of spent fuel and preferable to leaving large concentrations of spent fuel in cooling tanks. The first dry storage installation in the US was licensed by the Nuclear Regulatory Commission (NRC) in 1986 at the Surry Nuclear Power Plant in Virginia. Spent fuel is currently stored in dry cask systems at a growing number of power plant sites, and at an interim facility located at the Idaho National Laboratory near Idaho Falls, Idaho. The NRC estimated that many of the nuclear power plants in the United States will be out of room in their spent fuel pools by 2015, most likely requiring the use of temporary storage of some kind. Yucca Mountain, in Nevada, was expected to open in 2017. However, on March 5, 2009, Energy Secretary Steven Chu reiterated in a Senate hearing that the Yucca Mountain site was no longer considered an option for storing reactor waste.
The 2008, NRC guidelines call for fuels to have spent at least five years in a storage pool before being moved to dry casks. The industry norm is about 10 years. The NRC describes the dry casks used in the US as "designed to resist floods, tornadoes, projectiles, temperature extremes, and other unusual scenarios."
As of the end of 2009, 13,856 metric tons of commercial spent fuel – or about 22% – were stored in dry casks.
In the 1990s, the NRC had to “take repeated actions to address defective welds on dry casks that led to cracks and quality assurance problems; helium had leaked into some casks, increasing temperatures and causing accelerated fuel corrosion”.
With the zeroing of the federal budget for the Yucca Mountain nuclear waste repository in Nevada, more nuclear waste is being loaded into sealed metal casks filled with inert gas. Many of these casks will be stored in coastal or lakeside regions where a salt air environment exists, and the Massachusetts Institute of Technology is studying how such dry casks perform in salt environments. Cracking related to corrosion could occur in 30 years or less, and the NRC is studying whether the casks can be used for 100 years as some hope.
According to the NRC's website in 2023, spent fuel placed in dry cask storage from the Diablo Canyon power plant in California shows no sign of corrosion after more than a decade of storage and appears to be capable of lasting for 1800 years before succumbing to corrosion. Company videos, covering the processes and remote handling, from the initial fuel loading to the removal and eventual dry-cask storage, are viewable on various video hosting domains.
Canada
In Canada, above-ground dry storage has been used. Ontario Power Generation is in the process of constructing a Dry Storage Cask storage facility on its Darlington site, which will be similar in many respects to existing facilities at Pickering Nuclear Generating Station and Bruce Nuclear Generating Station. NB Power's Point Lepreau Nuclear Generating Station and Hydro-Québec's Gentilly Nuclear Generating Station also both operate dry storage facilities.
Germany
A centralized storage facility using dry casks is located at Ahaus. As of 2011, it housed 311 casks: 305 from the Thorium High Temperature Reactor, 3 from the Neckarwestheim Nuclear Power Plant, and 3 from the Gundremmingen Nuclear Power Plant. The transport from Gundremmingen to the Ahaus site met with considerable public protest and the power plant operators and the government later agreed to locate such casks at the powerplants.
CASTOR () is a trademarked brand of dry casks used to store spent nuclear fuel (a type of nuclear waste). CASTORs are manufactured by Gesellschaft für Nuklear-Service (GNS), a German provider of nuclear services.
CONSTOR is a cask used for transport and long-term storage of spent fuel and high-level waste also manufactured by GNS. Its inner and outer layers are steel, enclosing a layer of concrete. A 9-meter drop test of the V/TC model was conducted in 2004; the results conformed to expectations.
Bulgaria
In 2008, officials at the Kozloduy Nuclear Power Plant announced their intention to use 34 CONSTOR casks at the Kozloduy NPP site before the end of 2010.
Lithuania
Spent fuel from the now-closed Ignalina Nuclear Power Plant was placed in CASTOR and CONSTOR storage casks during the 2000s.
Russia
The Russian dry storage facility for spent nuclear fuel, the HOT-2 at Mining Chemical Combine in Zheleznogorsk, Krasnoyarsk Krai in Siberia, is not a 'cask' facility per se, as it is designed to accommodate the spent nuclear fuel (both VVER and RBMK) in a series of compartments. The structure of the facility is made up of monolithic reinforced concrete walls and top and bottom slabs, with the actual storage compartments formed by reinforced concrete partitions. The fuel is to be cooled by natural convection of air. The design capacity of the facility is 37,785 tonnes of uranium. It is now under construction and in the process of commissioning.
Ukraine
In Ukraine, a dry storage facility has been accepting spent fuel from the six-unit Zaporizhzhia Nuclear Power Plant (VVER-1000 reactors) since 2001, making it the longest-serving such facility in the former Soviet Union. The system was designed by the now-defunct Duke Engineering of the United States, with the storage casks being manufactured locally.
Another project is underway with Holtec International (of the USA) to build a dry spent fuel storage facility at the 1986 accident Chernobyl Nuclear Power Plant (RBMK-1000 reactors). The project was initially started with Framatome (currently AREVA) of France, later suspended and terminated due to technical difficulties. Holtec was originally hired as a subcontractor to dehydrate the spent fuel, eventually taking over the entire project.
See also
Deep geological repository
Ducrete
Lists of nuclear disasters and radioactive incidents
Nuclear decommissioning
Nuclear flask
Private Fuel Storage, proposed storage in Utah
References
External links
NRC: Dry Cask Storage
United States Nuclear Waste Technical Review Board, Evaluation of the Technical Basis for Extended Dry Storage and Transportation of Used Nuclear Fuel 2010
Locations of Independent Spent Fuel Storage Installations
Radioactive waste
Waste treatment technology
Nuclear power plant components | Dry cask storage | [
"Chemistry",
"Technology",
"Engineering"
] | 1,795 | [
"Water treatment",
"Hazardous waste",
"Environmental impact of nuclear power",
"Radioactivity",
"Environmental engineering",
"Waste treatment technology",
"Radioactive waste"
] |
363,483 | https://en.wikipedia.org/wiki/Augite | Augite, also known as Augurite, is a common rock-forming pyroxene mineral with formula . The crystals are monoclinic and prismatic. Augite has two prominent cleavages, meeting at angles near 90 degrees.
Characteristics
Augite is a solid solution in the pyroxene group. Diopside and hedenbergite are important endmembers in augite, but augite can also contain significant aluminium, titanium, and sodium and other elements. The calcium content of augite is limited by a miscibility gap between it and pigeonite and orthopyroxene: when occurring with either of these other pyroxenes, the calcium content of augite is a function of temperature and pressure, but mostly of temperature, and so can be useful in reconstructing temperature histories of rocks. With declining temperature, augite may exsolve lamellae of pigeonite and/or orthopyroxene. There is also a miscibility gap between augite and omphacite, but this gap occurs at higher temperatures. There are no industrial or economic uses for this mineral.
Locations
Augite is an essential mineral in mafic igneous rocks; for example, gabbro and basalt and common in ultramafic rocks. It also occurs in relatively high-temperature metamorphic rocks such as mafic granulite and metamorphosed iron formations. It commonly occurs in association with orthoclase, sanidine, labradorite, olivine, leucite, amphiboles and other pyroxenes.
Occasional specimens have a shiny appearance that give rise to the mineral's name, which is from the Greek augites, meaning "brightness", although ordinary specimens have a dull (dark green, brown or black) luster. It was named by Abraham Gottlob Werner in 1792.
See also
Fassaite
References
Further reading
Deer, W. A., Howie, R. A., and Zussman, J. (1992). An introduction to the rock-forming minerals (2nd ed.). Harlow: Longman
Sodium minerals
Calcium minerals
Magnesium minerals
Iron minerals
Pyroxene group
Monoclinic minerals
Minerals in space group 15
Gemstones
Minerals described in 1792 | Augite | [
"Physics"
] | 470 | [
"Materials",
"Gemstones",
"Matter"
] |
363,523 | https://en.wikipedia.org/wiki/Colombeau%20algebra | In mathematics, a Colombeau algebra is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this.
Such a multiplication of distributions has long been believed to be impossible because of L. Schwartz' impossibility result, which basically states that there cannot be a differential algebra containing the space of distributions and preserving the product of continuous functions. However, if one only wants to preserve the product of smooth functions instead such a construction becomes possible, as demonstrated first by Colombeau.
As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory. These algebras have found numerous applications in the fields of partial differential equations, geophysics, microlocal analysis and general relativity so far .
Colombeau algebras are named after French mathematician Jean François Colombeau.
Schwartz' impossibility result
Attempting to embed the space of distributions on into an associative algebra , the following requirements seem to be natural:
is linearly embedded into such that the constant function becomes the unity in ,
There is a partial derivative operator on which is linear and satisfies the Leibniz rule,
the restriction of to coincides with the usual partial derivative,
the restriction of to coincides with the pointwise product.
However, L. Schwartz' result implies that these requirements cannot hold simultaneously. The same is true even if, in 4., one replaces by , the space of times continuously differentiable functions. While this result has often been interpreted as saying that a general multiplication of distributions is not possible, in fact it only states that one cannot unrestrictedly combine differentiation, multiplication of continuous functions and the presence of singular objects like the Dirac delta.
Colombeau algebras are constructed to satisfy conditions 1.–3. and a condition like 4., but with replaced by , i.e., they preserve the product of smooth (infinitely differentiable) functions only.
Basic idea
The Colombeau Algebra is defined as the quotient algebra
Here the algebra of moderate functions on is the algebra of families of smooth regularisations (fε)
of smooth functions on
(where R+ = (0,∞) is the "regularization" parameter ε), such that for all compact subsets K of and all multiindices α, there is an N > 0 such that
The ideal of negligible functions is defined in the same way but with the partial derivatives instead bounded by O(ε+N) for all N > 0.
Embedding of distributions
The space(s) of Schwartz distributions can be embedded into the simplified algebra by (component-wise) convolution with any element of the algebra having as representative a δ-net, i.e. a family of smooth functions such that in D' as ε → 0.
This embedding is non-canonical, because it depends on the choice of the δ-net. However, there are versions of Colombeau algebras (so called full algebras) which allow for canonical embeddings of distributions. A well known full version is obtained by adding the mollifiers as second indexing set.
See also
Generalized function
Notes
References
Colombeau, J. F., New Generalized Functions and Multiplication of the Distributions. North Holland, Amsterdam, 1984.
Colombeau, J. F., Elementary introduction to new generalized functions. North-Holland, Amsterdam, 1985.
Nedeljkov, M., Pilipović, S., Scarpalezos, D., Linear Theory of Colombeau's Generalized Functions, Addison Wesley, Longman, 1998.
Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R.; Geometric Theory of Generalized Functions with Applications to General Relativity, Springer Series Mathematics and Its Applications, Vol. 537, 2002; .
Smooth functions
Functional analysis
Algebras
Schwartz distributions | Colombeau algebra | [
"Mathematics"
] | 838 | [
"Functions and mappings",
"Mathematical structures",
"Functional analysis",
"Algebras",
"Mathematical objects",
"Algebraic structures",
"Mathematical relations"
] |
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