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Lucas number
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Not to be confused with Lucas sequences, a generic class of sequences to which the Lucas numbers belong.
This article's lead section does not adequately summarize key points of its contents. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. Please discuss this issue on the article's talk page. (November 2015)
The Lucas spiral, made with quarter-arcs, is a good approximation of the golden spiral when its terms are large. However, when its terms become very small, the arc's radius decreases rapidly from 3 to 1 then increases from 1 to 2.
The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences.
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but instead of starting with 1 and 2, the Lucas sequence starts with 1 and 3. This produces a sequence where the ratios of successive terms approach the golden ratio, as the terms themselves are roundings of integer powers of the golden ratio.[1] They also have a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between.[2]
Contents
1 Definition
2 Extension to negative integers
3 Relationship to Fibonacci numbers
4 Congruence relations
5 Lucas primes
6 Generating series
7 Lucas polynomials
8 See also
9 References
10 External links
Definition[edit]
Similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, thereby forming a Fibonacci integer sequence. The first two Lucas numbers are L0 = 2 and L1 = 1 as opposed to the first two Fibonacci numbers F0 = 0 and F1 = 1. Though closely related in definition, Lucas and Fibonacci numbers exhibit distinct properties.
The Lucas numbers may thus be defined as follows:
L n := { 2 if n = 0 ; 1 if n = 1 ; L n − 1 + L n − 2 if n > 1. {\displaystyle L_{n}:={\begin{cases}2&{\text{if }}n=0;\\1&{\text{if }}n=1;\\L_{n-1}+L_{n-2}&{\text{if }}n>1.\\\end{cases}}}
(where n belongs to the natural numbers)
The sequence of Lucas numbers is:
2 , 1 , 3 , 4 , 7 , 11 , 18 , 29 , 47 , 76 , 123 , … {\displaystyle 2,\;1,\;3,\;4,\;7,\;11,\;18,\;29,\;47,\;76,\;123,\;\ldots \;} (sequence A000032 in the OEIS).
All Fibonacci-like integer sequences appear in shifted form as a row of the Wythoff array; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row. Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers converges to the golden ratio.
Extension to negative integers[edit]
Using Ln−2 = Ln − Ln−1, one can extend the Lucas numbers to negative integers to obtain a doubly infinite sequence:
..., −11, 7, −4, 3, −1, 2, 1, 3, 4, 7, 11, ... (terms L n {\displaystyle L_{n}} for − 5 ≤ n ≤ 5 {\displaystyle -5\leq {}n\leq 5} are shown).
The formula for terms with negative indices in this sequence is
L − n = ( − 1 ) n L n . {\displaystyle L_{-n}=(-1)^{n}L_{n}.\!}
Relationship to Fibonacci numbers[edit]
The Lucas numbers are related to the Fibonacci numbers by the identities
L n = F n − 1 + F n + 1 = F n + 2 F n − 1 = F n + 2 − F n − 2 {\displaystyle \,L_{n}=F_{n-1}+F_{n+1}=F_{n}+2F_{n-1}=F_{n+2}-F_{n-2}}
L m + n = L m + 1 F n + L m F n − 1 {\displaystyle \,L_{m+n}=L_{m+1}F_{n}+L_{m}F_{n-1}}
L n 2 = 5 F n 2 + 4 ( − 1 ) n {\displaystyle \,L_{n}^{2}=5F_{n}^{2}+4(-1)^{n}} , and thus as n {\displaystyle n\,} approaches +∞, the ratio L n F n {\displaystyle {\frac {L_{n}}{F_{n}}}} approaches 5 . {\displaystyle {\sqrt {5}}.}
F 2 n = L n F n {\displaystyle \,F_{2n}=L_{n}F_{n}}
F n + k + ( − 1 ) k F n − k = L k F n {\displaystyle \,F_{n+k}+(-1)^{k}F_{n-k}=L_{k}F_{n}}
F n = L n − 1 + L n + 1 5 = L n − 3 + L n + 3 10 {\displaystyle \,F_{n}={L_{n-1}+L_{n+1} \over 5}={L_{n-3}+L_{n+3} \over 10}}
Their closed formula is given as:
L n = φ n + ( 1 − φ ) n = φ n + ( − φ ) − n = ( 1 + 5 2 ) n + ( 1 − 5 2 ) n , {\displaystyle L_{n}=\varphi ^{n}+(1-\varphi )^{n}=\varphi ^{n}+(-\varphi )^{-n}=\left({1+{\sqrt {5}} \over 2}\right)^{n}+\left({1-{\sqrt {5}} \over 2}\right)^{n}\,,}
where φ {\displaystyle \varphi } is the golden ratio. Alternatively, as for n > 1 {\displaystyle n>1} the magnitude of the term ( − φ ) − n {\displaystyle (-\varphi )^{-n}} is less than 1/2, L n {\displaystyle L_{n}} is the closest integer to φ n {\displaystyle \varphi ^{n}} or, equivalently, the integer part of φ n + 1 / 2 {\displaystyle \varphi ^{n}+1/2} , also written as ⌊ φ n + 1 / 2 ⌋ {\displaystyle \lfloor \varphi ^{n}+1/2\rfloor } .
Combining the above with Binet's formula,
F n = φ n − ( 1 − φ ) n 5 , {\displaystyle F_{n}={\frac {\varphi ^{n}-(1-\varphi )^{n}}{\sqrt {5}}}\,,}
a formula for φ n {\displaystyle \varphi ^{n}} is obtained:
φ n = L n + F n 5 2 . {\displaystyle \varphi ^{n}={{L_{n}+F_{n}{\sqrt {5}}} \over 2}\,.}
Congruence relations[edit]
If Fn ≥ 5 is a Fibonacci number then no Lucas number is divisible by Fn.
Ln is congruent to 1 mod n if n is prime, but some composite values of n also have this property. These are the Bruckman-Lucas pseudoprimes.
Lucas primes[edit]
A Lucas prime is a Lucas number that is prime. The first few Lucas primes are
2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, ... (sequence A005479 in the OEIS).
For these ns are
0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, ... (sequence A001606 in the OEIS).
If Ln is prime then n is either 0, prime, or a power of 2.[3] L2m is prime for m = 1, 2, 3, and 4 and no other known values of m.
Generating series[edit]
Let
Φ ( x ) = 2 + x + 3 x 2 + 4 x 3 + ⋯ = ∑ n = 0 ∞ L n x n {\displaystyle \Phi (x)=2+x+3x^{2}+4x^{3}+\cdots =\sum _{n=0}^{\infty }L_{n}x^{n}}
be the generating series of the Lucas numbers. By a direct computation,
Φ ( x ) = L 0 + L 1 x + ∑ n = 2 ∞ L n x n = 2 + x + ∑ n = 2 ∞ ( L n − 1 + L n − 2 ) x n = 2 + x + ∑ n = 1 ∞ L n x n + 1 + ∑ n = 0 ∞ L n x n + 2 = 2 + x + x ( Φ ( x ) − 2 ) + x 2 Φ ( x ) {\displaystyle {\begin{aligned}\Phi (x)&=L_{0}+L_{1}x+\sum _{n=2}^{\infty }L_{n}x^{n}\\&=2+x+\sum _{n=2}^{\infty }(L_{n-1}+L_{n-2})x^{n}\\&=2+x+\sum _{n=1}^{\infty }L_{n}x^{n+1}+\sum _{n=0}^{\infty }L_{n}x^{n+2}\\&=2+x+x(\Phi (x)-2)+x^{2}\Phi (x)\end{aligned}}}
which can be rearranged as
Φ ( x ) = 2 − x 1 − x − x 2 . {\displaystyle \Phi (x)={\frac {2-x}{1-x-x^{2}}}.}

The partial fraction decomposition is given by
Φ ( x ) = 1 1 − φ x + 1 1 − ϕ x {\displaystyle \Phi (x)={\frac {1}{1-\varphi x}}+{\frac {1}{1-\phi x}}}
where φ = 1 + 5 2 {\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}} is the golden ratio and ϕ = 1 − 5 2 {\displaystyle \phi ={\frac {1-{\sqrt {5}}}{2}}} is its conjugate.
Lucas polynomials[edit]
In the same way as Fibonacci polynomials are derived from the Fibonacci numbers, the Lucas polynomials Ln(x) are a polynomial sequence derived from the Lucas numbers.
See also[edit]
Fibonacci number
Fibonacci prime
Golden ratio
References[edit]
Jump up ^ Parker, Matt (2014). "13". Things to Make and Do in the Fourth Dimension. Farrar, Straus and Giroux. p. 284. ISBN 978-0-374-53563-6. |access-date= requires |url= (help)
Jump up ^ Parker, Matt (2014). "13". Things to Make and Do in the Fourth Dimension. Farrar, Straus and Giroux. p. 282. ISBN 978-0-374-53563-6. |access-date= requires |url= (help)
Jump up ^ Chris Caldwell, "The Prime Glossary: Lucas prime" from The Prime Pages.
External links[edit]
Hazewinkel, Michiel, ed. (2001) [1994], "Lucas polynomials", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Weisstein, Eric W. "Lucas Number". MathWorld.
Weisstein, Eric W. "Lucas Polynomial". MathWorld.
Dr Ron Knott
Lucas numbers and the Golden Section
A Lucas Number Calculator can be found here.
OEIS sequence A000032 (Lucas numbers beginning at 2)
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Chief of Staff of the United States Air Force
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Chief of Staff of the Air Force
CSAF or CC/AF
Seal of the Chief of Staff
Flag of the Chief of Staff
Incumbent
General David L. Goldfein
since July 1, 2016
Department of the Air Force
The Air Staff
Member of
Joint Chiefs of Staff
Reports to
Secretary of Defense
Secretary of the Air Force
Appointer
The President
with Senate advice and consent
Term length
4 years
Renewable
Constituting instrument
10 U.S.C. § 8033
Precursor
Commanding General, United States Army Air Forces
Formation
September 18, 1947
First holder
Carl A. Spaatz
Deputy
Vice Chief of Staff of the Air Force
Website
Official Website
The Chief of Staff of the Air Force (acronym: CSAF, or AF/CC) is a statutory office (10 U.S.C. § 8033) held by a four-star general in the United States Air Force, and is the most senior uniformed officer assigned to serve in the Department of the Air Force, and as such is the principal military advisor and a deputy to the Secretary of the Air Force; and is in a separate capacity a member of the Joint Chiefs of Staff, and thereby a military adviser to the National Security Council, the Secretary of Defense, and the President. The Chief of Staff is typically the highest-ranking officer on active-duty in the U.S. Air Force unless the Chairman and/or the Vice Chairman of the Joint Chiefs of Staff are Air Force officers.
The Chief of Staff of the Air Force is an administrative position based in the Pentagon, and while the Chief of Staff does not have operational command authority over Air Force forces (that is within the purview of the Combatant Commanders who report to the Secretary of Defense), the Chief of Staff does exercise supervision of Air Force units and organizations as the designee of the Secretary of the Air Force.
The current Chief of Staff of the Air Force is General David L. Goldfein.
Contents
[hide]
1 Responsibilities
1.1 Department of the Air Force
1.2 Member of the Joint Chiefs of Staff
2 Appointment and rank
2.1 Special uniform cap
3 List of Chiefs of Staff, U.S. Air Force (1947–present)
4 See also
5 References
5.1 Notes
6 External links
Responsibilities[edit]
Department of the Air Force[edit]
Under the authority, direction and control of the Secretary of the Air Force, the Chief of Staff presides over the Air Staff, acts as the Secretary's executive agent in carrying out approved plans, and exercises supervision, consistent with authority assigned to Commanders of the Combatant Commands, over organizations and members of the Air Force as determined by the Secretary. The Chief of Staff may also perform other duties as assigned by either the President, the Secretary of Defense or the Secretary of the Air Force.[1]
The Vice Chief of Staff of the Air Force, also a four-star general, is the Chief of Staff's principal deputy.[2]
Member of the Joint Chiefs of Staff[edit]
The Chief of Staff of the Air Force is a member of the Joint Chiefs of Staff as prescribed by 10 U.S.C. § 151. When performing his JCS duties the Chief of Staff is responsible directly to the Secretary of Defense. Like the other members of the Joint Chiefs of Staff, the CSAF is an administrative position, with no operational command authority over the United States Air Force.
Appointment and rank[edit]
The CSAF is nominated for appointment by the President and must be confirmed via majority vote by the Senate.[1] By statute, the CSAF is appointed as a four-star general.[1]
Special uniform cap[edit]
The Chief of Staff is also authorized to wear a special service cap with clouds and lightning bolts around the band of the hat. This cap is different from those worn by other general officers of the Air Force and it is for use by the Chief of Staff and Air Force officers serving as Chairman or Vice Chairman of the Joint Chiefs of Staff.
List of Chiefs of Staff, U.S. Air Force (1947–present)[edit]
Prior to the creation of this position, General Henry H. Arnold was designated first Chief of the Army Air Forces and Commanding General of the Army Air Forces during World War II.
No.
Image
Name
Term of Office
Primary Background
Secretaries served under:
Began
Ended
Days of Service
Air Force
Defense
1 Carl A. Spaatz September 26, 1947 April 29, 1948 216 Fighters Stuart Symington James Forrestal
2 Hoyt S. Vandenberg April 30, 1948 June 29, 1953 1887 Attack and Fighters Stuart Symington
Thomas K. Finletter
Harold E. Talbott James Forrestal
Louis A. Johnson
George C. Marshall
Robert A. Lovett
Charles E. Wilson
3 Nathan F. Twining* June 30, 1953 June 30, 1957 1461 Fighters and Bombers Harold E. Talbott
Donald A. Quarles
James H. Douglas, Jr. Charles E. Wilson
4 Thomas D. White July 1, 1957 June 30, 1961 1460 Observation aircraft and Staff James H. Douglas, Jr.
Dudley C. Sharp
Eugene M. Zuckert Charles E. Wilson
Neil H. McElroy
Thomas S. Gates
Robert S. McNamara
5 Curtis E. LeMay June 30, 1961 January 31, 1965 1311 Bombers Eugene M. Zuckert Robert S. McNamara
6 John P. McConnell February 1, 1965 July 31, 1969 1641 Fighters Eugene M. Zuckert
Harold Brown
Robert C. Seamans, Jr. Robert S. McNamara
Clark M. Clifford
Melvin R. Laird
7 John D. Ryan August 1, 1969 July 31, 1973 1460 Bombers Robert C. Seamans, Jr.
John L. McLucas Melvin R. Laird
Elliot Richardson
James R. Schlesinger
8 George S. Brown* August 1, 1973 June 30, 1974 333 Bombers John L. McLucas James R. Schlesinger
9 David C. Jones* July 1, 1974 June 20, 1978 1450 Bombers John L. McLucas
Thomas C. Reed
John C. Stetson James R. Schlesinger
Donald H. Rumsfeld
Harold Brown
10 Lew Allen Jr. July 1, 1978 June 30, 1982 1460 Bombers John C. Stetson
Hans Mark
Verne Orr Harold Brown
Caspar Weinberger
11 Charles A. Gabriel July 1, 1982 June 30, 1986 1460 Fighters Verne Orr
Russell A. Rourke
Edward C. Aldridge Jr. Caspar Weinberger
12 Larry D. Welch July 1, 1986 June 30, 1990 1460 Fighters Edward C. Aldridge Jr.
Donald B. Rice Caspar Weinberger
Frank Carlucci
Dick Cheney
13 Michael J. Dugan July 1, 1990 September 17, 1990 78 Fighters Donald B. Rice Dick Cheney
(Acting) John M. Loh September 18, 1990 October 29, 1990 41 Fighters
14 Merrill A. McPeak October 30, 1990 October 25, 1994 1456 Fighters Donald B. Rice
Sheila E. Widnall Dick Cheney
Les Aspin
William J. Perry
15 Ronald R. Fogleman October 26, 1994 September 1, 1997 1041 Fighters Sheila E. Widnall William J. Perry
William S. Cohen
(Acting) Ralph E. Eberhart September 2, 1997 October 5, 1997[3] 33 Fighters William S. Cohen
16 Michael E. Ryan October 6, 1997 September 5, 2001 1430 Fighters Sheila E. Widnall
F. Whitten Peters
James G. Roche William S. Cohen
Donald H. Rumsfeld
17 John P. Jumper September 6, 2001 September 2, 2005 1457 Fighters James G. Roche Donald H. Rumsfeld
18 T. Michael Moseley September 2, 2005 July 12, 2008[4][5] 1044 Fighters Michael Wynne Donald H. Rumsfeld
Robert M. Gates
(Acting) Duncan J. McNabb July 12, 2008 August 12, 2008[5] 31 Airlift Michael B. Donley Robert M. Gates
19 Norton A. Schwartz August 12, 2008 August 10, 2012 1459 Airlift and Special Operations aircraft Michael B. Donley Robert M. Gates
Leon Panetta
20 Mark A. Welsh III August 10, 2012 June 24, 2016 1414 Attack and Fighters Michael B. Donley
Deborah Lee James Leon Panetta
Chuck Hagel
Ashton Carter
21 David L. Goldfein July 1, 2016 Incumbent 549 Fighters Deborah Lee James
Heather Wilson Ashton Carter
James Mattis
*Three former chiefs of staff would later serve as Chairman of the Joint Chiefs of Staff:
Twining served as the Chairman from August 1957 to September 1960.
Brown served as the Chairman from July 1974 to June 1978.
Jones served as the Chairman from June 1978 to June 1982.
The fourth Air Force officer to have served as the Chairman, General Richard B. Myers, did not serve as Chief of Staff of the Air Force.
McPeak is the only Chief of Staff of the Air Force to date who has served as Acting Secretary of the Air Force (from July 14, 1993 to August 5, 1993 before Sheila Widnall took office as Secretary), thus being the only uniformed Air Force officer to have truly been the "head of the Air Force".
See also[edit]
United States Air Force portal
Vice Chief of Staff of the United States Air Force
Chief Master Sergeant of the Air Force
References[edit]
Department of Defense Key Officials 1947–2015 (PDF). Washington DC: Office of the Secretary of Defense, Historical Office. 2015.
HAF MISSION DIRECTIVE 1-4 - CHIEF OF STAFF OF THE AIR FORCE (PDF). Washington DC: Secretary of the Air Force. 7 March 2012.
Headquarters United States Air Force Key Personnel (PDF). Washington DC: Air Force Historical Studies Office. January 2013.
Notes[edit]
^ Jump up to: a b c [1] 10 USC 8033. Chief of Staff
Jump up ^ [2] 10 USC 8034. Vice Chief of Staff
Jump up ^ [3], Accessed on 2011-09-12
Jump up ^ [4]
^ Jump up to: a b [5]
External links[edit]
Air Force History Support Office: Air Force Chiefs of Staff
[show]
v
t
e
Chiefs of Staff of the Air Force
Spaatz
Vandenberg
Twining
White
LeMay
McConnell
J. D. Ryan
Brown
Jones
Allen
Gabriel
Welch
Dugan
Loh (acting)
McPeak
Fogleman
Eberhart (acting)
M. E. Ryan
Jumper
Moseley
McNabb (acting)
Schwartz
Welsh
Goldfein
[show]
v
t
e
Senior officials in the United States Department of Defense
Secretary of Defense
Jim Mattis
Deputy Secretary of Defense
Patrick Shanahan
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Secretary of the Army: Mark Esper
Secretary of the Navy: Richard V. Spencer
Secretary of the Air Force: Heather Wilson
Chairman of the Joint Chiefs of Staff
Gen Joe Dunford, USMC
Under Secretaries of Defense for

Acquisition, Technology and Logistics: Ellen Lord
Policy: David Trachtenberga
Comptroller/Chief Financial Officer: David Norquist
Personnel and Readiness: Robert Wilkie
Intelligence: Joseph D. Kernan
Deputy Chief Management Officer
John H. Gibson
Vice Chairman of the Joint Chiefs of Staff
Gen Paul Selva, USAF
Chiefs of the Military Services

Chief of Staff of the Army: GEN Mark Milley
Commandant of the Marine Corps: Gen Robert Neller
Chief of Naval Operations: ADM John Richardson
Chief of Staff of the Air Force: Gen David Goldfein
Chief of the National Guard Bureau
Gen Joseph Lengyel, USAF
Unified Combatant Command Commanders

Africa: Gen Tom Waldhauser, USMC
Central: GEN Joe Votel, USA
European: GEN Mike Scaparrotti, USA
Northern: Gen Lori Robinson, USAF
Pacific: ADM Harry Harris, USN
Southern: ADM Kurt Tidd, USN
Special Operations: GEN Tony Thomas, USA
Strategic: Gen John Hyten, USAF
Transportation: Gen Darren McDew, USAF
a - Acting
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Input/output
From Wikipedia, the free encyclopedia
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"I/O" redirects here. For other uses, see I/O (disambiguation).
For uses of the term input-output in economics, see Input-output model.
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2016) (Learn how and when to remove this template message)
Operating systems
Common features
Process management
Interrupts
Memory management
File system
Device drivers
Networking
Security
I/O
v
t
e
In computing, input/output or I/O (or, informally, io or IO) is the communication between an information processing system, such as a computer, and the outside world, possibly a human or another information processing system. Inputs are the signals or data received by the system and outputs are the signals or data sent from it. The term can also be used as part of an action; to "perform I/O" is to perform an input or output operation.
I/O devices are the pieces of hardware used by a human (or other system) to communicate with a computer. For instance, a keyboard or computer mouse is an input device for a computer, while monitors and printers are output devices. Devices for communication between computers, such as modems and network cards, typically perform both input and output operations.
The designation of a device as either input or output depends on perspective. Mouse and keyboards take physical movements that the human user outputs and convert them into input signals that a computer can understand; the output from these devices is the computer's input. Similarly, printers and monitors take signals that a computer outputs as input, and they convert these signals into a representation that human users can understand. From the human user's perspective, the process of reading or seeing these representations is receiving input; this type of interaction between computers and humans is studied in the field of human–computer interaction.
In computer architecture, the combination of the CPU and main memory, to which the CPU can read or write directly using individual instructions, is considered the brain of a computer. Any transfer of information to or from the CPU/memory combo, for example by reading data from a disk drive, is considered I/O.[1] The CPU and its supporting circuitry may provide memory-mapped I/O that is used in low-level computer programming, such as in the implementation of device drivers, or may provide access to I/O channels. An I/O algorithm is one designed to exploit locality and perform efficiently when exchanging data with a secondary storage device, such as a disk drive.
Contents
[hide]
1 Interface
1.1 Higher-level implementation
2 Channel I/O
3 Port-mapped I/O
4 See also
5 References
Interface[edit]
An I/O interface is required whenever the I/O device is driven by the processor. Typically a CPU communicates with devices via a bus. The interface must have necessary logic to interpret the device address generated by the processor. Handshaking should be implemented by the interface using appropriate commands (like BUSY, READY, and WAIT), and the processor can communicate with an I/O device through the interface. If different data formats are being exchanged, the interface must be able to convert serial data to parallel form and vice versa. Because it would be a waste for a processor to be idle while it waits for data from an input device there must be provision for generating interrupts[2] and the corresponding type numbers for further processing by the processor if required.[clarification needed]
A computer that uses memory-mapped I/O accesses hardware by reading and writing to specific memory locations, using the same assembly language instructions that computer would normally use to access memory. An alternative method is via instruction-based I/O which requires that a CPU have specialised instructions for I/O.[1] Both input and output devices have a data processing rate that can vary greatly.[2] With some devices able to exchange data at very high speeds direct access to memory (DMA) without the continuous aid of a CPU is required.[2]
Higher-level implementation[edit]
Higher-level operating system and programming facilities employ separate, more abstract I/O concepts and primitives. For example, most operating systems provide application programs with the concept of files. The C and C++ programming languages, and operating systems in the Unix family, traditionally abstract files and devices as streams, which can be read or written, or sometimes both. The C standard library provides functions for manipulating streams for input and output.
In the context of the ALGOL 68 programming language, the input and output facilities are collectively referred to as transput. The ALGOL 68 transput library recognizes the following standard files/devices: stand in, stand out, stand errors and stand back.
An alternative to special primitive functions is the I/O monad, which permits programs to just describe I/O, and the actions are carried out outside the program. This is notable because the I/O functions would introduce side-effects to any programming language, but this allows purely functional programming to be practical.
Channel I/O[edit]
Channel I/O requires the use of instructions that are specifically designed to perform I/O operations. The I/O instructions address the channel or the channel and device; the channel asynchronously accesses all other required addressing and control information. This is similar to DMA, but more flexible.
Port-mapped I/O[edit]
Port-mapped I/O also requires the use of special I/O instructions. Typically one or more ports are assigned to the device, each with a special purpose. The port numbers are in a separate address space from that used by normal instructions.
See also[edit]
Information Technology portal
Asynchronous I/O
I/O bound
BASIC § Input and output
References[edit]
^ Jump up to: a b Null, Linda; Julia Lobur (2006). The Essentials of Computer Organization and Architecture. Jones & Bartlett Learning. p. 185. ISBN 0763737690. Retrieved 11 December 2016.
^ Jump up to: a b c Abd-El-Barr, Mostafa; Hesham El-Rewini (2005). Fundamentals of Computer Organization and Architecture. John Wiley & Sons. p. 161-162. ISBN 9780471478331. Retrieved 11 December 2016.
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Mineral wool
From Wikipedia, the free encyclopedia
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This article's lead section may not adequately summarize key points of its contents. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. Please discuss this issue on the article's talk page. (October 2016)
Mineral wool close-up.
Mineral wool under microscope
Building joint with incomplete firestop made of mineral wool packing that still requires topcaulking.
Common insulation applications in an apartment building.
Mineral wool pipe covering applied to a steel pipe for a fire test.
Mineral wool is a general name for fiber materials that are formed by spinning or drawing molten minerals (or "synthetic minerals" such as slag and ceramics).[1]
Applications of mineral wool include thermal insulation (as both structural insulation and pipe insulation, though it is not as fire-resistant as high-temperature insulation wool), filtration, soundproofing, and hydroponic growth medium.
Contents
[hide]
1 Naming
2 History
3 Manufacture
4 Usage
4.1 In hydroponics
5 Safety of material
6 See also
7 References
8 External links
Naming[edit]
Mineral wool is also known as mineral fiber, mineral cotton, mineral fibre, man-made mineral fibre (MMMF), and man-made vitreous fiber (MMVF).
The nomenclature of these wool products is simply the parent/raw material name in prefix to "wool". Specific mineral wool products are stone wool and slag wool. Europe also includes glass wool which, together with ceramic fiber, are completely man-made fibers.
History[edit]
Slag wool was first made in 1840 in Wales by Edward Parry, "but no effort appears to have been made to confine the wool after production; consequently it floated about the works with the slightest breeze, and became so injurious to the men that the process had to be abandoned".[2] A method of making mineral wool was patented in the United States in 1870 by John Player[3] and first produced commercially in 1871 at Georgsmarienhütte in Osnabrück Germany. The process involved blowing a strong stream of air across a falling flow of liquid iron slag which was similar to the natural occurrence of fine strands of volcanic slag from Kilauea called Pele's hair created by strong winds blowing apart the slag during an eruption.[3]
American chemical engineer Charles Corydon Hall in 1897 developed a technology to convert molten limestone into fibers and initiated the rock wool insulation industry in America.
Manufacture[edit]
Stone wool is a furnace product of molten rock at a temperature of about 1600 °C, through which a stream of air or steam is blown. More advanced production techniques are based on spinning molten rock in high-speed spinning heads somewhat like the process used to produce cotton candy. The final product is a mass of fine, intertwined fibres with a typical diameter of 2 to 6 micrometers. Mineral wool may contain a binder, often a terpolymer, and an oil to reduce dusting.
Usage[edit]
Though the individual fibers conduct heat very well, when pressed into rolls and sheets, their ability to partition air makes them excellent insulators and sound absorbers.[4][5] Though not immune to the effects of a sufficiently hot fire, the fire resistance of fiberglass, stone wool, and ceramic fibers makes them common building materials when passive fire protection is required, being used as spray fireproofing, in stud cavities in drywall assemblies and as packing materials in firestops.
Other uses are in resin bonded panels, as filler in compounds for gaskets, in brake pads, in plastics in the automotive industry, as a filtering medium, and as a growth medium in hydroponics.
Mineral fibers are produced in the same way, without binder. The fiber as such is used as a raw material for its reinforcing purposes in various applications, such as friction materials, gaskets, plastics, and coatings.
Heat resistance of mineral wool[6]
Material
Temperature
Glass wool 230 – 260 °C
Stone wool 700 – 850 °C
Ceramic fiber wool 1200 °C
In hydroponics[edit]
Mineral wool products can be engineered to hold large quantities of water and air that aid root growth and nutrient uptake in hydroponics; their fibrous nature also provides a good mechanical structure to hold the plant stable. The naturally high pH of mineral wool makes them initially unsuitable to plant growth and requires "conditioning" to produce a wool with an appropriate, stable pH.[7]:16
Safety of material[edit]
The International Agency for Research on Cancer (IARC) has reviewed the carcinogenicity of man-made mineral fibres in October 2002.[8] The IARC Monograph's working group concluded only the more biopersistent materials remain classified by IARC as "possibly carcinogenic to humans" (Group 2B). These include refractory ceramic fibres, which are used industrially as insulation in high-temperature environments such as blast furnaces, and certain special-purpose glass wools not used as insulating materials. In contrast, the more commonly used vitreous fibre wools produced since 2000, including insulation glass wool, stone wool, and slag wool, are considered "not classifiable as to carcinogenicity in humans" (Group 3).
High biosoluble fibres are produced that do not cause damage to the human cell. These newer materials have been tested for carcinogenicity and most are found to be noncarcinogenic. IARC elected not to make an overall evaluation of the newly developed fibres designed to be less biopersistent such as the alkaline earth silicate or high-alumina, low-silica wools. This decision was made in part because no human data were available, although such fibres that have been tested appear to have low carcinogenic potential in experimental animals, and because the Working Group had difficulty in categorizing these fibres into meaningful groups based on chemical composition."[9]
The European Regulation (CE) n° 1272/2008 on classification, labelling and packaging of substances and mixtures updated by the Regulation (CE) n°790/2009 does not classify mineral wool fibres as a dangerous substance if they fulfil criteria defined in its note Q.
The European Certification Board for mineral wool products, EUCEB, certify mineral wool products made of fibres fulfilling Note Q ensuring that they have a low biopersistence and so that they are fast removed from the lung. The certification is based on independent experts’ advice and regular control of the chemical composition www.euceb.org
Due to the mechanical effect of fibres, mineral wool products may cause temporary skin itching. To diminish this and to avoid unnecessary exposure to mineral wool dust, information on good practices is available on the packaging of mineral wool products with pictograms or sentences. Safe Use Instruction Sheets similar to Safety data sheet are also available from each producer.
People can be exposed to mineral wool fibers in the workplace by breathing them in, skin contact, and eye contact. The Occupational Safety and Health Administration (OSHA) has set the legal limit (permissible exposure limit) for mineral wool fiber exposure in the workplace as 15 mg/m3 total exposure and 5 mg/m3 respiratory exposure over an 8-hour workday. The National Institute for Occupational Safety and Health (NIOSH) has set a recommended exposure limit (REL) of 5 mg/m3 total exposure and 3 fibers per cm3 over an 8-hour workday.[10]
See also[edit]
Risk and Safety Statements
Basalt fiber, a mineral fiber having high tensile strength
Asbestos, a mineral that is naturally fibrous
Pele's hair
Glass wool
References[edit]
Jump up ^ "Man-made mineral fibre (MMMF) is a generic name used to describe an inorganic fibrous material manufactured primarily from glass, rock, minerals, slag and processed inorganic. The MMMF produced are non-crystalline (glassy, vitreous, amorphous)." [1] Recommendation from the Scientific Committee on Occupational Exposure Limits for man made-mineral fibres (MMMF) with no indication for carcinogenicity and not specified elsewhere
Jump up ^ Spon, Ernest. Workshop Receipts ... London: E. & F. N. Spon, 18831892. Page 439
^ Jump up to: a b "Mineral Wool or Mineral Cotton", Appleton's Annual Cyclopedia and Register of Important Events of the Year 1891. New Series vol. 16. New York: 1892. 528. Print.
Jump up ^ Weiner, Ethan. Acoustic Treatment and Design for Recording Studios and Listening Rooms. "Without question, the most effective absorber for midrange and high frequencies is rigid fiberglass."http://www.ethanwiner.com/acoustics.html#rigid%20fiberglass.
Jump up ^ Houghton, Matt. Sound On Sound. "What is the best density for a good, fairly wide-spectrum absorber? . . .try looking for mineral wool in the region of 45-75kg/m3." http://www.soundonsound.com/sos/oct10/articles/qa-1010-2.htm
Jump up ^ "Competition Commission Alternatives to Glass Mineral Wool" (PDF). 090820 competition-commission.org.uk, 2.2 Mineral Wools
Jump up ^ Tom Alexander; Don Parker (1994). The Best of Growing Edge. New Moon Publishing, Inc. ISBN 978-0-944557-01-3.
Jump up ^ IARC Monographs on the Evaluation of Carcinogenic Risks to Humans, Volume 81 (2002), Man-made Vitreous Fibres (PLEASE NOTE: Some manufacturers of insulation products[who?] have cited this volume while making erroneous claims that "IARC scientists confirm safety of mineral wool insulation". These claims are just false. The findings in this volume are not a determination of non-carcinogenicity or overall safety.)
Jump up ^ IARC Monographs on the Evaluation of Carcinogenic Risks to Humans, Volume 81 (2002), Man-made Vitreous Fibres, Overall evaluation, p. 339
Jump up ^ "CDC – NIOSH Pocket Guide to Chemical Hazards – Mineral wool fiber". www.cdc.gov. Retrieved 2015-11-27.
External links[edit]
Wikimedia Commons has media related to Mineral wool.
Wikisource has the text of a 1905 New International Encyclopedia article about Mineral wool.
Statistics Canada documents on shipments of mineral wool in Canada
Review of published data on exposure to mineral wool during installation work by A Jones and A Sanchez Jimenez, Institute of Occupational Medicine Research Report TM/11/01
Assessment of airborne mineral wool fibres in domestic houses by J Dodgson and others. Institute of Occupational Medicine Research Report TM/87/18
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