text:
Talk:Electromagnet

Left-hand rule vs Right-hand rule
I changed the part about the left-hand rule giving the direction of the magnetic field inside a solenoid - definitely not the case! Magnetic flux inside a solenoid follows the right-hand rule. (I'm sure one or two people got one or two answers wrong in their test!) —The preceding unsigned comment was added by 125.237.23.198 (talk) 08:39, 9 May 2007 (UTC).

Your Dates Were Way Off
Excuse me for being vociferous, but William Sturgeon died in 1850. Yes, he did invent the electromagnet. He actually invented much earlier than you indicated. He invented it in 1823. Michael Faraday wouldn't have been able to create his electric motor in the 1830s if William Sturgeon hadn't invented the electromagnet in 1823, because an electromagnet is one of the essential components of an electric motor. In 1837, Samuel Morse invented the electromagnetic telegraph, which is an electromagnet that pulls an iron tapper towards it when an electric current is flowing through the wire. The electric telegraph is an electromagnet that creates clicks by pulling an iron tapper. This tapping is similar to the clicks produced by the electromagnetic relay, which was invented in 1835 by Joseph Henry.

The electromagnet was invented long before the year you had written.

Electromagnets&school
This site doesn't have enough data for our school project on electromagnets.

 * Try using other sources. --Smack (talk) 22:26, 12 May 2005 (UTC)

 * This attitude is the very reason why Wikipedia is sooo useless. That is why people don't donate: we can't use it. Here, it doesn't show how to calculate the force excerted on a piece of iron by the magnetic force at 'd' distance from the coil. All academic bull, no practical use. — Preceding unsigned comment added by 115.70.177.64 (talk) 13:53, 16 July 2013 (UTC)

 * If someone could come up with some drawings and images, I can do the math. Something simple, like a U-bolt from a hardware store would be nice. Or simpler yet, a square core with one end cut off. Please don't include the standard nail example -- it's way too hard to analyze in closed form. Here are a couple of example from Edmunds Scientific. Madhu 00:13, 31 October 2005 (UTC)

 * If you're talking about a closed magnetic circuit, such as an electromagnet of wire wound on a U-shaped bolt picking up a steel plate bridged across its poles, eq. (1) and (2) in the article can be used. You can calculate the magnetic field B from the number of turns and the current using eq. (1) if you measure the length of the looping magnetic path L through the bolt and the plate,  provided you can find the magnetic permeability μ of the steel.    Then eq. (2) will give you the force exerted by each pole face on the steel plate,  from the area A of the pole face.  The main problem will be finding the permeability of the steel.  I'd just go on the Internet and use a value for mild steel.  It won't be very accurate, but you will be within a factor of two.  -- Chetvorno TALK 14:32, 16 July 2013 (UTC)

Applications
I think an intereseting application of electro-magnets is in its use as a weapon, namely rail guns.

Yeah, the incredibly high magnetic field needed to make a heavy object shoot out of the electromagnet will leave tumours in your brain, apart from killing another person with the weapon, but why use springs or air pressure or maybe even gunpowder in your gun for a better, cheaper, safer result, not to mention the exclusion of the necessity to plug your "weapon" into a wall socket. How about junkyards? They seem to lift pretty heavy objects with those electromagnetic cranes. Slartibartfast1992 23:51, 13 March 2007 (UTC)

Another place of use in the ag industry are in electric clutches so pumps or shafts can be turned on and off immediately with the flick of a switch. — Preceding unsigned comment added by Kenton007 (talk • contribs) 13:49, 5 May 2013 (UTC)

who
who made this page

 * Lots of people. See the history page. --Smack (talk) 05:11, 6 October 2005 (UTC)

Force on Ferromag Materials calculation?
The force per unit area is given in lbft/in2, when all the quantities that go into the calculation are in SI. If I do the calculation in SI units, the F/A comes out to 398 kN/m2 for the 1 Tesla case.

Does anyone else agree that we should have consistent units all the way through those calculations? --Syrthiss 02:58, 28 October 2005 (UTC)

 * Sure, include the SI numbers. The only reason I used mixed units is that most people don't have a feel for what a kN/m^2 (kPa) is. All I ask is that you keep the mixed unit numbers since it's easy to get your head around PSI. Think of it this way: I need to lift 50 pounds, how big of a magnet do I need? 1 Tesla is a reasonable number for flux density, so a square inch is in the ballpark. In SI, 50 pounds (force) is about 200 N, so you would need some very small area in m^2. Square centimeters would be easier, a centimeter is easy to guestimate. I like to run numbers in my head or the back of an envelope... Madhu 00:05, 31 October 2005 (UTC)

 * I think we should insist on SI. Add American units in parentheses if you want, but it's counterproductive to perpetuate them. --Smack (talk) 22:43, 11 November 2005 (UTC)

WHERE is the calculation of force exerted on ferromagnetic magetic material across an air gap???? I've looked everywhere and I can't find it.

Thecoolsundar (talk) 07:28, 15 August 2010 (UTC)

Another question
Come to think of it, what is this section doing in an article on electromagnetism? Shouldn't it be somewhere else, like ferromagnetism? --Smack (talk) 04:59, 16 November 2005 (UTC)

 * Well, I think he was using it as a basis for how to calculate the turnings and such an electromagnet would need to develop a field of XX strength. So, yes it could be used in Ferromagnetism but also seems applicable here.  That reminds me though, I need to put in the SI calculations.  Then we can still consider whether to move it or leave it here. --Syrthiss 05:32, 16 November 2005 (UTC)

 * Done. I just looove Mathcad. It has to be one of the greatest software applications ever developed. Madhu 01:48, 17 November 2005 (UTC)

 * Thanks :) --Syrthiss 04:44, 17 November 2005 (UTC)

could you tell me more about magnetic calculations?thanking you,rudrakshm@pathways.ac.in

 * Sure, it's simple. The fundamental definition of energy is force times distance. The energy in a magnetic field can be derived from first principles, you can find that in any electromagnetics text. Fields and Waves in Communication Electronics by Ramo, Whinnery, and Van Duzer is an excellent book. If you have a magnetic field of a known field strength, you can calculate the energy of that field. If anything is added to that field that changes the field strength, the energy changes. To change the energy requires a force, which is energy divided by change in distance (or dE/dx to be more accurate). I assumed the field was in air, but it could be in any medium. The derivation is in Magnetic_field Madhu 17:25, 18 November 2005 (UTC)

I need to create a electrical magnet that can preform the operations od a linear actuator EG propel the inner rod with reasonable force but not exceeding the stroke. I do not waht the rod to fly out im trying to achieve a popper like motion when a current is applied can anyone help?

Remanent magnetism
The article should include something about remanent magnetism.

What happened to the image?
What happened to the cool image of an industrial lifting electromagnet? Why was that removed? Madhu 20:50, 11 August 2006 (UTC)

Higher ampere-turns
You say there is no point in using more than 787 A-turns per metre (not sure exactly where this figure comes from), because of saturation of the electromagnet core. However this only happens when the air gap of the magnet is closed. If you want to project a large field into an air gap, rather than just hold onto a chunk of iron, then I think you can usefully use a far larger mmf per length of core because the dominant reluctance of the air gap lowers the H field.

Simon80.41.41.166 23:37, 31 August 2006 (UTC)

 * That value is rougly the saturation field intensity for steel. You are correct about projecting large fields into an air gap. Feel free to adjust the wording as appropriate. Madhu 03:08, 1 September 2006 (UTC)

 * Done. -- Chetvorno TALK 19:30, 27 September 2008 (UTC)

What about force between Electromagnets
Somebody Please include the description on force calculation between the electromagnets ( attractive or repulsive ).

vijay anand

 * WP:SOFIXIT. -- 19:26, 11 February 2008 (UTC)

field redirection?
Does anyone know how one could block the field in one direction and/or amplify the field in the other direction? 71.185.202.190 (talk) 22:19, 1 May 2008 (UTC)

Possible error: paramagnetic core?
The Introduction section says Much stronger magnetic fields can be produced if a "core" of paramagnetic or ferromagnetic material (commonly soft iron) is placed inside the coil. Paramagnetic? I've never heard of a paramagnetic material being used for the core of an electromagnet, at least not to increase it's permeability. Yes, a paramagnetic material would produce a slightly greater H than no core, but the increase is of the order 10-5, totally negligible. Even if paramagnetic cores have been used for some specialized research purposes, I think it is misleading to list it next to and on an equal basis with 'ferromagnetic'. All ordinary electromagnets use ferromagnetic cores. Unless there's a good reason for leaving it in, I'm going to delete it. -- Chetvorno TALK 05:52, 9 August 2008 (UTC)

 * Done -- Chetvorno TALK 23:33, 12 August 2008 (UTC)

Air gap?
Where? Air gap between turns? Air gap between winding and core? Air gap between sections of core? The latter makes sense from the discussion but isnt at first obvious. All terms should be clarified with a diagram or description, as one does with an equation. Small ambiguities can lead to hours of futility for a practical desighn engineer where accurate information has to be applied to create working systems. —Preceding unsigned comment added by Q5101997 (talk • contribs) 02:48, 17 December 2008 (UTC)
 * Thanks, you're right, that's unclear. Its the air gap between sections of the core.  I was going to include a diagram of an electromagnet illustrating air gaps, fringing fields, and leakage flux, but didn't get around to it. -- Chetvorno TALK 03:31, 17 December 2008 (UTC)
 * Added diagram clarifying the above terms. -- Chetvorno TALK 15:01, 6 October 2010 (UTC)

Reply to Air Gap?
Your article was very informative and accurate. The use of diagrams and explanations of terms is imperitive. Contininuue to elaborate on this and it will be a fine and usefull article. 124.177.127.47 (talk) 10:56, 22 December 2008 (UTC)

hi —Preceding unsigned comment added by 99.251.238.177 (talk) 14:24, 6 February 2010 (UTC)

Removal of content in "Ohmic heating" section
A 15:59, May 14 edit by 94.237.95.24 removed the discussion of minimum heat dissipation in the "Ohmic heating" section with this comment: "It was forgotten that when N increases -> also R increases due to increased length. Further analysis based on this misconception all removed."  I reverted this removal; the original content was correct. Below is a derivation of the disputed point: that the ohmic heat losses in an electromagnet can be reduced by increasing the number of turns and proportionately decreasing the current, but that there is a minimum imposed by the area available for the windings. This is shown in many texts on electric machinery; I'll try to find a source.

The total resistance R of a DC electromagnet's windings is given by:

$$R = \frac {\rho L}{a} = \frac {\rho N l}{a} $$

where $$\rho$$ is the resistivity of the wire, $$L$$ is the total length of the winding, $$l$$ is the average length of one turn, $$N$$ is the number of turns, and $$a$$ is the cross-sectional area of the wire. So the total power dissipation $$P$$ due to ohmic heating is:

$$P = I^2 R = I^2 \frac {\rho N l}{a} \qquad \qquad (1)$$

As discussed in the article, the magnetic field produced by the magnet is a function of the magnetomotive force $$\mathfrak F = NI$$ so $$N$$ and $$I$$ can be varied to minimize the power dissipation as long as their product is constant. Substituting for $$I$$ into (1):

$$P = \left ( \frac {\mathfrak F}{N} \right )^2 \frac {\rho N l}{a} = \frac { \mathfrak F^2 \rho l}{Na} \qquad \qquad (2)$$

So the power dissipation is inversely proportional to $$N$$. Thus the heat losses can be minimized by increasing the number of turns, while decreasing the current proportionally to keep $$\mathfrak F$$ constant. It would seem that the dissipation could by reduced indefinitely this way. However the product $$Na$$ in the denominator is equal to the cross-sectional area of the winding (ignoring insulation thickness and wasted space). It increases with $$N$$. There is some limit to the area available between the arms of the core for the winding, call it $$A$$. Therefore $$Na \leq A \,$$. Substituting (2) into this:

$$P \geq \frac { \mathfrak F^2 \rho l}{A} $$

This is the minimum ohmic heat dissipation of a resistive electromagnet. To show that the minimum dissipation increases with $$B^2$$ the Faraday law expression for a closed core electromagnet (eq. (1) from the article) can be used:

$$NI = \mathfrak F = \frac {B}{\mu} $$

So:

$$P \geq \frac {B^2 \rho l}{\mu^2 A} $$

-- Chetvorno TALK 05:15, 16 May 2010 (UTC)

"Loudsmpeakers?"
I can't seem to correct this error in the first paragraph. Anyone with more Wiki mojo want to try? Pammalamma (talk) 03:59, 20 November 2010 (UTC)

Image
Perhaps that the image to the right can be added to this article ? 91.182.255.53 (talk) 14:39, 2 February 2011 (UTC)
 * No. They would add nothing, it's also confusing (you were told this just a couple of days ago) to describe motor field coils as "electromagnets" (although they are, they're used to generate a field which reacts wiith another field, not for their simple attractiveness to magnetic materials). Andy Dingley (talk) 15:01, 2 February 2011 (UTC)
 * I've also tagged the image for deletion - or maybe we should categorize it under "impossible objects"? Is that bottom-left coil a left- or right-handed helix? Andy Dingley (talk) 15:25, 2 February 2011 (UTC)

Force between electromagnets
Can someone put in what the terms of the force between electromagnets refer to. It might seem intuitive but i cant figure out whats 'A'. I assume it has to be an area but what area? 59.191.202.234 (talk) 02:27, 26 February 2012 (UTC)
 * And also there is no mention of the Ampere model in that section Malithyapa (talk) 02:28, 26 February 2012 (UTC)
 * A is the cross-sectional area of the magnetic pole, which is the cross sectional area of the core; see the "Definition of terms" box at the end of the article. The "Ampere model" is primarily a way to explain how permanent magnets work and the term isn't used much with electromagnets. -- Chetvorno TALK 02:55, 26 February 2012 (UTC)

Edit request on 19 March 2012
Add iw link Sähkömagneetti

Jawacz (talk) 18:54, 19 March 2012 (UTC)
 * Yes check.svg Done - completed. Keith D (talk) 21:30, 19 March 2012 (UTC)

Electro-permanent magnet
I expected to find something about electro-permanent magnets in this article ... are they called something else here, perhaps? quota (talk) 07:21, 6 April 2012 (UTC)

Force between electromagnets
In the section for force between electromagnets, the force calculation omits any reference to the magnetic permeability of the core. The force between two electromagnets will certainly depend upon the identity of the core. If the core is air, the magnetic flux density will be small. Add soft iron or something of the sort and the magnetic flux density will be huge. I believe the F equation should us mu instead of mu_0, where mu is the magnetic permeability of the core. Am I missing something here? — Preceding unsigned comment added by 24.228.19.137 (talk) 20:16, 18 February 2013 (UTC)
 * In Eq. 4, the F equation, the permeability of the core is accounted for by the μ2 in the numerator. It also has μ0 in the denominator, as you noted, which makes it a little confusing. -- Chetvorno TALK 19:05, 9 April 2013 (UTC)

Depiction of magnetic field
Hello. In Electromagnet with gap.svg there are some field lines with begin and end, magnetic field lines form loops or extend infinitely in both directions, they don't form loops (Gauss's law for magnetism). I understand that the computation required to make an accurate representation of a magnetic field isn't trivial, but even not taking the image as an quantitative depiction of a magnetic field (Its description says than it isn't) this is an important conceptual flaw. QrTTf7fH (talk) 01:52, 31 July 2014 (UTC).
 * Hi, I drew that diagram. Are you talking about the leakage flux lines, labeled BL, between the two vertical arms of the core? -- Chetvorno TALK 02:30, 31 July 2014 (UTC)
 * Thanks for your reply. Indeed those are the lines I'm talking about. QrTTf7fH (talk) 22:50, 4 August 2014 (UTC).
 * Well, I agree with you. I tried a couple of drawings to get the full leakage flux lines in, but they messed up the drawing so much that I did them this way.  You have to remember that this drawing is designed to illustrate the text's "constant B field" approximation, used to analyze modern magnetic circuits in which the leakage flux is insignificant, so the B flux is assumed constant throughout the core.  The number of leakage flux lines is exaggerated in this picture.   Putting in those full leakage flux lines made it look like the density of B field lines varied around the core loop, and I thought that would be confusing for readers trying to understand the equations.  Most of the field lines in the image do form closed loops, and I thought it would be clear from context that the incomplete ones did too. -- Chetvorno TALK 00:56, 5 August 2014 (UTC)

The term "ferromagnetic" in the introduction
About the recent changes. I feel an important point to make in the introduction for nontechnical readers is that the magnetic-core electromagnet is a ferromagnetic device; the necessary quality in the core is that it be ferromagnetic or ferrimagnetic. The theory behind the iron-core electromagnet, and thus all its incredibly important applications in modern society; motors, generators, transformers, and magnetic storage, is ferromagnetism. It should be mentioned in the intro. It's important to get it straight because there are several other types of magnetism in physics, paramagnetism and diamagnetism, which can confuse newbies. It's not enough to say the magnet is called a ferromagnetic-core electromagnet, it should be stated the core must be ferromagnetic. -- Chetvorno TALK 23:34, 15 September 2014 (UTC)
 * Chetvorno: Free feel to restore your edit, but I'd encourage you to avoid redundancy within a single paragraph. In my opinion, that needs to be fixed and that's why I undid it. Maybe I have made a mistake by undoing it outright rather than just pointing this problem. I don't object to make clear the role of ferromagnetism. Also take into account air core electromagnets. There may exist the convention to call those those not electromagnets, but only coils even though the principle of operation is almost the same. I don't know what's the predominant convention. Regards and thanks for contributing. QrTTf7fH (talk) 01:09, 16 September 2014 (UTC).

 * I believe air-core electromagnets are usually called solenoids, as the introduction says, although I have no objection to the term "air-core electromagnet" if you want to add it. If by redundancy you mean using the term "ferromagnetic-core electromagnet" in addition to the previous references to ferromagnetism, the latter is just making sure readers know the commonly used technical terms for electromagnets.  Cheers,  Chetvorno TALK 01:40, 16 September 2014 (UTC)

 * A solenoid is a particular shape of electromagnet; air-cored electromagnets need not be solenoids.GliderMaven (talk) 02:24, 16 September 2014 (UTC)

 * Actually, that the core is ferromagnetic or ferrimagnetic is not sufficient (and I'm not sure off-hand whether it's necessary either, but I can't think of a counterexample). A magnetic core, suitable for an electromagnet for good performance really does have to be soft. There's plenty of ferromagnetic or ferrimagnetic materials that are very hard, and they are hardly ever acceptable for use as cores, as they perform virtually no better than air cores.GliderMaven (talk) 02:24, 16 September 2014 (UTC)
 * I understand that. I have no problem with also saying that the core must be a soft ferromagnetic material, but the most important property is that it is ferromagnetic or ferrimagnetic.  Only ferromagnetic or ferrimagnetic materials have the high permeability required for all the important applications of electromagnets: motors, generators, etc.   This is important basic science for the general reader.   Here are some citations that electromagnet cores are ferromagnetic:  1,  2, 3,    4, 5, 6, p.4, 7 -- Chetvorno TALK 08:26, 16 September 2014 (UTC)
 * Why don't you just write magnetically soft ferromagnetic or ferrimagnetic material? That would solve the problem, wouldn't it? YohanN7 (talk) 09:32, 16 September 2014 (UTC)
 * That would be fine with me. -- Chetvorno TALK 11:46, 16 September 2014 (UTC)

 * It's still pretty rubbish. The point of the article is to try to explain how electromagnets work mainly for people who don't know. Simply stating that such and such a material is used isn't very good at all. You're much better off mentioning the typical requirements for a magnetic core material (high saturation and low susceptibility, only not necessarily using those words without defining them) and then giving a common example (iron). We have an entire article on magnetic cores anyway which can go into much more detail.GliderMaven (talk) 14:00, 16 September 2014 (UTC)

 * And I would question the usage of the term 'ferromagnetic material' unless you also define it first, 99% of the time, if you know what it means then you don't need to read the article anyway.GliderMaven (talk) 14:00, 16 September 2014 (UTC)
 * If the ancillary properties "saturation" and "susceptibility" are important for people to know, isn't the basic property "ferromagnetism" more important, without which the core will not work at all? You can't increase the field of an electromagnet (measurably) by inserting a core of wood.    On the issue of defining ferromagnetism, the second section takes care of that.  They can also click on the link to the article.  Other examples of ferromagnetic core materials, such as ferrite could be mentioned.

 * I'm surprised there is any controversy about this.   Other articles on ferromagnetic devices like Permanent magnet mention ferromagnetism up front.   Ferro- (or ferri-) magnetism is the defining property of electromagnet cores.    If I were an educator, that's one of the main points I'd want general readers to take away from the introduction. -- Chetvorno TALK 18:07, 16 September 2014 (UTC)

 * I don't think that's right. We're not just trying to create an article consisting of random facts. Why isn't wood any good? If we do it your way, the reader wouldn't know, it's not bad simply because it's not ferromagnetic.

 * Suppose a new material was created tomorrow using material science, magnetinium that works in a new way. Could you use it for a magnetic core for an electromagnet or not? According to what you want to write, you couldn't, solely because it's neither ferromagnetic nor ferrimagnetic. Are all ferromagnetic materials good for electromagnets? No, they're not. Hard ferromagnetic materials are useless. But not all ferromagnetic soft materials are necessarily very good either. If they have low saturation or poor permeability they're not very good in most case. And ferromagnetic materials vary very widely. In fact, most alloys are going to be pretty useless, even if technically ferromagnetic. Also other properties like conductivity are very bad. Ferromagnetic materials often have high conductivity; you usually don't really want that either.

 * We want the reader to understand which materials are likely to be good, irrespective of whether they're ferromagnetic or not, the underlying cause of the magnetism is nothing much to do with it.GliderMaven (talk) 20:04, 16 September 2014 (UTC)

 * You don't believe that the magnetic core in an electromagnet must be ferromagnetic or ferrimagnetic to increase the permeability? -- Chetvorno TALK 22:02, 16 September 2014 (UTC)

 * That's roughly correct.GliderMaven (talk) 23:06, 16 September 2014 (UTC)
 * Look at the references I gave above. Here are some more: 8,  9,  10. -- Chetvorno TALK 05:45, 17 September 2014 (UTC)

From a purely WP:LEAD point of view, the article has several sections devoted to cores and the requirement for ferromagnetism is stated prominently. It is a reasonable summary to have the ferromagnetic core requirement in the lead. The argument that not all ferromagnetic materials make good cores is irrelevant to the statement that all cores must be ferromagnetic. This is the logical fallacy of denying the antecedent; all A are B is not invalidated because some B are not A. That some new material for cores might be discovered that is not ferromagnetic is WP:CRYSTAL and also irrelevant, certainly not encyclopaedia worthy. I am not convinced that there are any genuine electromagnet applications of air-cored solenoids. The solenoid in its actuator role has a metal armature which is effectively acting as a core. SpinningSpark 09:52, 17 September 2014 (UTC)

 * If only what you said was true, I would have let it go, but not only are not all ferromagnetic materials suitable, but not only ferromagnetic materials are successfully used; specifically, ferrites are used for high frequency electromagnets, and are not ferromagnetic.GliderMaven (talk) 13:38, 17 September 2014 (UTC)

 * So it is not correct to state, or imply that only ferromagnetic cores can be used, which is what Chetvorno has been consistently doing.GliderMaven (talk) 13:45, 17 September 2014 (UTC)
 * No, if you will look at my statements to you above, I included ferrimagnetic materials:
 * "the necessary quality in the core is that it be ferromagnetic or ferrimagnetic."
 * "Ferro- (or ferri-) magnetism is the defining property of electromagnet cores."
 * "Only ferromagnetic or ferrimagnetic materials have the high permeability required..."
 * The wording of the introduction which I am supporting and you objected to and changed said "Much stronger magnetic fields can be produced if a "magnetic core" of a ferromagnetic (or ferrimagnetic) material, such as iron, is placed inside the coil" -- Chetvorno TALK 14:28, 17 September 2014 (UTC)
 * Since with Spinningspark, YohanN7,   QrTTf7fH, and lastly  GliderMaven's above statements it looks like there is consensus on the use of the terms "ferromagnetic" and "ferrimagnetic" in the intro, I restored the compromise wording suggested by YohanN7 above and added supporting citations. -- Chetvorno TALK 16:10, 20 September 2014 (UTC)
 * I think the reason for this misunderstanding is that the term "magnetic materials" is usually used for core materials in engineering texts and sources, to avoid having to write "ferromagnetic and ferrimagnetic materials" all the time. So the terms "ferromagnetic" and "ferrimagnetic" don't appear much. -- Chetvorno TALK 16:31, 20 September 2014 (UTC)
 * I still don't agree, but the bigger problem is that you are essentially trying to put a spin into the article that magnetic cores are the most important thing about electromagnets and that cores are ferromagnetic and hence ferromagnetism is the most important thing.

 * The problem with that is, try telling that to someone who has cancer and needs an MRI machine!!! Cores are not useful at high flux levels. The idea that air cored electromagnets don't matter, is a value judgement you're trying to impose on the article, and is unequivocally incorrect. Commonality and importance are NOT the same thing!

 * By doing that, you're distorting the article, very many features of electromagnets are common to both magnetic and non magnetic cores, but by trying to write the article in either-or terms that becomes almost impossible to deal with.GliderMaven (talk) 13:33, 22 September 2014 (UTC)

 * OK, I see the problem. Back in 2010 an anonymous broke lots of things and removed the introduction section. Rather than revert it, it was fixed up, which left the magnetic core section stranded. The problem with moving material into the lead is that it's not really repeated elsewhere, you're not supposed to only cover material in the lead, the lead is supposed to be a summary of the article not do the work for the article in describing how electromagnets are constructed.GliderMaven (talk) 14:53, 22 September 2014 (UTC)

Thanks GliderMaven! Does it look ok now? Is the lead as informative as we all would like? Gryllida (talk) 04:05, 23 September 2014 (UTC)

 * I think as discussed above the introduction needs to indicate what the magnetic core is made of, that it must be ferromagnetic (or ferrimagnetic). This is the defining property of the iron-core electromagnet and an important basic science take-away for general readers.   All of the 10 references given above introduce the electromagnet as a ferromagnetic device.  As SpinningSpark noted above, most of the article is devoted to analyzing the ferromagnetic-core electromagnet, so from WP:LEAD the introduction should mention the term.  It was originally in the introduction, but User:GliderMaven edited it to remove the term. -- Chetvorno TALK 11:09, 23 September 2014 (UTC)
 * "I don't object to make clear the role of ferromagnetism." from QrTTf7fH above suggests that we can add it. Please go ahead and do so, and see if you can put it in a way which doesn't clutter the lead. Gryllida (talk) 11:35, 23 September 2014 (UTC)

GliderMaven has again removed the term "ferromagnetic" from the introduction. This is the defining property of an electromagnet core, and the consensus reached above is that due to its prominence in the article (most of the physics section is devoted to analyzing ferromagnetic core electromagnets) it should be in the introduction per WP:LEAD. -- Chetvorno TALK 21:44, 25 July 2015 (UTC)

 * Thanks, GliderMaven. -- Chetvorno TALK 22:16, 25 July 2015 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on Electromagnet. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20120220030524/http://instruct.tri-c.edu/fgram/web/Mdipole.htm to http://instruct.tri-c.edu/fgram/web/mdipole.htm

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.— InternetArchiveBot  (Report bug) 07:10, 22 December 2016 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified one external link on Electromagnet. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20100709205321/http://geophysics.ou.edu/solid_earth/notes/mag_basic/mag_basic.html to http://geophysics.ou.edu/solid_earth/notes/mag_basic/mag_basic.html

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 03:26, 19 September 2017 (UTC)

Electro magnet
What is a device that change the direction of the current in an electro magnet 196.188.112.67 (talk) 18:16, 28 March 2022 (UTC)
 * It's a current source. This section will be deleted, as it does not discuss content of the article. For any questions, please go to a forum. --Geek3 (talk) 19:22, 28 March 2022 (UTC)

title: Talk:Electromagnet


text:
User:Robin Hood~enwiki

Statistics
Created on 17th of May, 2004 Member no 68 840  users on 29 2024

af:Gebruiker:Robin Hood als:Benutzer:Robin Hood ar:مستخدم:Robin Hood az:İstifadəçi:Robin Hood

be-x-old:Удзельнік:Robin_Hood bg:Потребител:Robin Hood bs:Korisnik:Robin Hood ca:Usuari:Robin Hood cs:Wikipedista:Robin Hood cy:Defnyddiwr:Robin Hood da:Bruger:Robin Hood de:Benutzer:Robin Hood el:Χρήστης:Robin Hood eo:Vikipediisto:Robin Hood es:Usuario:Robin Hood et:Kasutaja:Robin Hood eu:Lankide:Robin Hood fa:کاربر:Robin Hood fi:Käyttäjä:Robin Hood fr:Utilisateur:Robin Hood gd:User:Robin Hood gl:User:Robin Hood he:משתמש:Robin Hood hr:Suradnik:Robin Hood hu:User:Robin Hood ia:Usator:Robin Hood id:Pengguna:Robin Hood is:Notandi:Robin Hood it:Utente:Robin Hood ja:利用者:Robin Hood ko:사용자:Robin Hood la:Usor:Robin Hood lb:User:Robin Hood li:Gebroeker:Robin Hood lt:Naudotojas:Robin Hood lv:Lietotājs:Robin Hood mk:Корисник:Robin Hood nl:Gebruiker:Robin Hood nn:Brukar:Robin Hood no:Bruker:Robin Hood pl:Wikipedysta:Robin Hood pt:Usuário:Robin Hood ro:Utilizator:Robin Hood ru:Участник:Robin Hood sh:User:Robin Hood sk:Redaktor:Robin Hood sl:Uporabnik:Robin Hood sr:Корисник:Robin Hood sv:Användare:Robin Hood tl:User:Robin Hood tr:Kullanıcı:Robin Hood uk:Користувач:Robin Hood ur:صارف:Robin Hood vi:Thành viên:Robin Hood zh:User:Robin Hood

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Robin Hood~enwiki


text:
Ent Air Force Base

Ent Air Force Base was a United States Air Force base located in the Knob Hill neighborhood of Colorado Springs, Colorado. A tent city, established in 1943 during construction of the base, was initially commanded by Major General Uzal Girard Ent (1900–1948), for whom the base is named. The base was opened in 1951.

From 1957 to 1963, the base was the site of North American Aerospace Defense Command (NORAD), which subsequently moved to the Cheyenne Mountain Air Force Station. The base became the Ent Annex to the Cheyenne Mountain facility in 1975. The base was closed in 1976. The site later became the location of the United States Olympic Training Center, which was completed in July 1978.

Background
The first Air Defense Command was established on 26 February 1940, by the War Department. On 2 March 1940, it was put under the First Army Commander. It managed air defense within four geographic air districts. It was inactivated in mid-1944 when the threat of air attack seemed minimal.

With the beginning of the Cold War, American defense experts and political leaders began planning and implementing a defensive air shield, which they believed was necessary to defend against a possible attack by long-range, manned Soviet bombers. The Air Defense Command was established 21 March 1946 and the major command was established at Mitchel Field (later Mitchel Air Force Base) in New York on 27 March 1946, which was commanded by Lieutenant General George E. Stratemeyer.

By the time of the United States Air Force creation in 1947, as a separate service, it was widely acknowledged the Air Force would be the center point of this defensive effort. The Air Force established the Continental Air Command under both the Air Defense Command and Tactical Air Command on 1 December 1948, at which time Commanding General Gordon P. Saville (later Major General) took command. The Air Defense Command was inactivated as a major command on 1 July 1950. The Air Defense Command was reconstituted by the United States Air Force 1 January 1951, to protect the United States air space, with two geographically based organizations. The portion of the country east of the 103rd meridian was managed by the Eastern Air Defense Force (also First Air Force territory). The command for the Western Air Defense Force (also Second Air Force territory) was at Ent Air Force Base. The functions included an early warning system to identify and respond to impending air attacks, including fighter interception. Subordinate Air Force commands were given responsibility to protect the various regions of the United States.

Colorado Springs Tent Camp
The Colorado Springs Tent Camp was the headquarters for the Second Air Force beginning early June 1943. It was moved from Fort George Wright in the state of Washington to the more central location within the western half of the United States—the Second Air Force territory. The tent city was used for soldiers who worked on the conversion of the National Methodist Sanatorium for military use and construction of additional buildings for the base. Beginning in 1943, the Second Air Force was commanded by Major General Uzal Girard Ent who became the Commanding General after having been the Chief of Staff. Ent retired due to disability in the line of duty, due to injuries he sustained in a B-25 crash in October 1944 during takeoff. He died on 5 March 1948. Major General Robert B. Williams became the commanding officer of the Second Air Force in October 1944; he retired 1 July 1946.

The facility became inactive when the 15th Air Force headquarters was assigned to March Air Force Base in November 1949. There were discussions about the city taking over the now unused property, but in November 1950, it was announced that the base was to become the headquarters for the Air Defense Command.

Air Defense Command
On 1 January 1951, the Air Defense Command was reestablished at Mitchel Air Force Base, under the command of Commanding General Ennis Whitehead, later lieutenant general. One week later the command was moved to Colorado Springs. The Ent Air Force Base, named for Major General Uzal Girard Ent, opened on 8 January 1951. The Air Defense Command (ADC) inherited 21 fighter squadrons from Continental Air Command (CONAD) and 37 Air National Guard (ANG) fighter squadrons assigned an M-Day air defense mission. It was also assigned four Air Divisions (Defense). General Benjamin W. Chidlaw was the base commander beginning 29 July 1951 and commander of the Air Defense Command from 25 August 1951 and until 31 May 1955.

The Senate appropriated an additional $3 million for expansion of the base in September 1951. The Peterson Air Force Base, which became inactive in 1949 when the 15th Air Force was moved to the March Air Force Base, was activated when the Ent Air Force Base opened. At the same time, the 4600th Air Base Group was activated to provide support for Ent. The funding was part of a military expansion initiative for the Ent Air Force Base, Fort Carson, and Peterson Air Force Base, all in Colorado Springs, Colorado. Much of the construction at Ent was for additional residential facilities. The Air Defense Command began 24-hour Ground Observer Corps operations on 14 July 1952. Starting September 1953, the base was the headquarters for the Army Anti-Aircraft Command.

Information about potential hostile aircraft from radar sites around the country was forwarded to a regional clearinghouse, like Otis Air National Guard Base, and then to ADC headquarters at Ent Air Force Base. It was then plotted on the world's largest Plexiglas board. Enemy bombers progress was tracked on the board using grease pencils. If there was a potential threat, interceptor aircraft were scrambled to the target. Because this process was cumbersome, it made a rapid response unattainable. An automated command and control system, Semi-Automatic Ground Environment (SAGE), based upon the Whirlwind II (AN/FSQ-7) computer was implemented to process ground radar and other sources for an immediate view of potential threats in the 1950s. There was an operational plan for a SAGE implementation for Ent by 7 March 1955.

A modern 15000 sqft concrete block Combat Operations Center (COC) became operational at the base on 15 May 1954. 1 September of that year, the Continental Air Defense Command (CONAD) was activated as a joint command at Ent AFB:
 * Air Defense Command was the United States Air Force component command
 * Army Antiaircraft Command was the Army component
 * Naval Forces CONAD was the Navy component (NAVFORCONAD), established at Ent. CONAD forces were committed to the Contiguous Radar Coverage System and of augmentation forces for all services made available during emergency periods.

The Colorado Springs Chamber of Commerce purchased 8.1 acres of land and donated it to the Ent Air Force Base, making it a permanent installation on 31 July 1954. In September of that year, the base became the headquarters of Continental Air Defense Command. More than $19 million was targeted in 1955 for further military expansion in the area, including the Fort Carson, the Ent Air Force Base, and the development of the Air Force Academy.

On 15 January 1956, General Earle E. Partridge, CINCONAD, directed his staff to begin preliminary planning for a Combat Operations Center to be located underground. Partridge believed his present above ground center, located on Ent Air Force Base was too small to manage the growing air defense system and was highly vulnerable to sabotage or attack. Partridge was made commander in 1955, was the driving force behind the creation of the Cheyenne Mountain Air Force Station. He requested an underground facility in December 1956.

Continental Air Command (CONAD) and the Air Defense Command (ADC) formally separated in 1956. Partridge was relieved of his command of CONAD and Lt. General Joseph H. Atkinson assumed control of ADC.

The Interceptor magazine was produced by the Air Defense Command at the Ent Air Force Base by 1959 and then the Aerospace Defense Command into the mid-1970s.

NORAD

The North American Air Defense Command (NORAD) was established and activated at the base on 12 September 1957. This command is an international organization, taking operational control of Canadian Air Defense Command air defense units and United States Air Defense Command air defense units. The first NORAD Agreement was drafted. Partridge was Commander-in-Chief, CONAD also became commander of NORAD. Royal Canadian Air Force Air Marshal Roy Slemon became deputy commander, NORAD. The official agreement between the two countries was signed 12 May 1958.

In 1958, the base put $36,904,558 into the Colorado Springs economy in the form of pay to 3,639 military and 1,222 civilian personnel and dependents allowances, which was more than $7 million more than the previous year. These numbers exclude individuals that work for 15 U.S. industries—such as Boeing and Lockheed Aircraft—on Ent. Due to improvements in radar technology, the Ground Observer Corps was inactivated on 31 July 1959.

The NORAD commander issued instructions on 21 April 1961, concerning the 425L command and control computer system operational philosophy, including use by NORAD and component personnel, NORAD entry to sufficiently enable him to evaluate indications presented, the requirements for human judgment in determining the validity of individual system indications, and identification of data as to source system.

Cheyenne Mountain transition
Excavation began for NORAD Command Operations Center (COC) in Cheyenne Mountain on 18 May 1961. The official ground breaking ceremony was held 16 June 1961 at the construction site of the new NORAD Combat Operations Center. Generals Lee (ADC) and Laurence S. Kuter (NORAD) simultaneously set off symbolic dynamite charges. Estimated cost of the combat operations center construction and equipment was $66 million.

Ent Annex
The 9th Aerospace Defense Division was activated at Ent Air Force Base on 15 July 1961. It was the first large military space organization in the western world. The first Aerospace Surveillance and Control Squadron were assigned to the 9 ADD.

The Air Defense Command's SPACETRACK Center and NORAD's Space Detection and Tracking System (SPADATS) Center merged to form the Space Defense Center. It was moved from Ent AFB to the newly completed Cheyenne Mountain Combat Operations Center and was activated on 3 September 1965.

A Major General was assigned as the first Director of the Combat Operations Center as recommended by the Cheyenne Mountain Complex Task Force Study Report on 1 October 1965. This established a separate Battle Staff organization. The Director was responsible directly to CINCNORAD for tactical matters and the Joint Chiefs of Staff for all others. CINCNORAD transferred Combat Operations Center operations from Ent Air Force Base to Cheyenne Mountain and declared the 425L command and control system fully operational 20 April 1966. On 20 May 1966, the NORAD Attack Warning System became operational. The Space Defense Center and the Combat Operations Center achieved Full Operational Capability on 6 February 1967. The total cost was $142.4 million.

The Fourteenth Aerospace Force was activated on 1 Jul 1968, at Ent AFB, Colorado. It inherited the staff and mission of the 9th Aerospace Defense Division, which was discontinued. The First Aerospace Control Squadron was then reassigned to the 14th Aerospace Force.

The Air Defense Command was re-designated as the Aerospace Defense Command on 15 January 1968. The Continental Air Defense Command and Aerospace Defense Command headquarters began consolidation and streamlining on 1 July 1973.

The Department of Defense announced plans for cutbacks in air defense forces showing increasing emphasis on ballistic missile attack warning and decreasing emphasis on bomber defense on 4 February 1974. The Continental Air Defense Command de-established on 30 June 1974.

Inactivation
The US Army Air Defense command, a component command of the North American Air Defense Command and Continental Air Command, was inactivated at Ent AFB, Colorado on 4 January 1975.

The 14th Aerospace Force, Ent AFB, Colorado was inactivated and its personnel and units (missile and space surveillance) were reassigned to HQ ADCOM and ADCOM divisions and the Alaskan ADCOM Region on 1 October 1976. Ent Air Force Base was declared excess. In December 1976, personnel were moved to Peterson Air Force Base and the Chidlaw Building, near downtown Colorado Springs. The Aerospace Defense Command was inactivated on 31 March 1980.

title: Ent Air Force Base


text:
Code completion

Code completion is an autocompletion feature in many integrated development environments (IDEs) that speeds up the process of coding applications by fixing common mistakes and suggesting lines of code. This usually happens through popups while typing, querying parameters of functions, and query hints related to syntax errors. Modern code completion software typically uses generative artificial intelligence systems to predict lines of code. Code completion and related tools serve as documentation and disambiguation for variable names, functions, and methods, using static analysis.

The feature appears in many programming environments. Implementations include IntelliSense in Visual Studio Code. The term was originally popularized as "picklist" and some implementations still refer to it as such.

Overview
Intelligent code completion, which is similar to other autocompletion systems, is a convenient way to access descriptions of functions—and in particular their parameter lists. The feature speeds up software development by reducing keyboard input and the necessity for name memorization. It also allows for users to refer less frequently to external documentation, as interactive documentation on many symbols (i.e. variables and functions) in the active scope appears dynamically in the form of tooltips.

Intelligent code completion uses an automatically generated in-memory database of classes, variable names, and other constructs that given computer code defines or references. The "classic" implementation of IntelliSense works by detecting marker characters such as periods (or other separator characters, depending on the language). When the user types one of these characters immediately after the name of an entity having one or more accessible members (such as contained variables or functions), IntelliSense suggests matches in a pop-up dialog. The user can either accept the suggestion by typing a statement-completion character ( or ) or a language-specific marker (such as the semicolon for C++), or continue typing the name. Over time, IntelliSense determines which variable or function the user most likely needs. IntelliSense also displays a short description of a function in the pop-up window—depending on the amount of documentation in the function's source code.

The feature also lets users select from a number of overloaded functions in languages that support object-oriented programming. Some code editing software provide intelligent code completion through a Language Server Protocol (LSP) server.

History
Research on intelligent code completion began in 1957, with spelling checkers for bitmap images of cursive writing and special applications to find records in databases despite incorrect entries. In 1961, Les Earnest, who headed the research on this budding technology, saw it necessary to include the first spell checker that accessed a list of 10,000 acceptable words. Ralph Gorin, a graduate student under Earnest at the time, created the first true spell-check program written as an application (rather than research) for general English text. SPELL, for the DEC PDP-10 at Stanford University's Artificial Intelligence Laboratory (SAIL), was published in February 1971. Gorin wrote the program in assembly for faster action; he made it by searching a word list for plausible correct spellings that differ by a single letter or adjacent-letter transpositions, and presenting them to the user. Gorin made SPELL publicly accessible, as was done with most SAIL programs, and it soon spread around the world via the then-new ARPANET, about a decade before personal computers came into general use. SPELL and its algorithms and data structures inspired the Unix program Ispell.

Visual Studio
IntelliSense is Microsoft's implementation of code completion, best known in Visual Studio. It was first introduced as a feature of a mainstream Microsoft product in 1996 building on many already invented concepts of code completion and syntax checking, with the Visual Basic 5.0 Control Creation Edition, which was essentially a publicly available prototype for Visual Basic 5.0. Initially, Visual Basic IDE was the primary "test bed" for the technology, but IntelliSense was incorporated into Visual FoxPro and Visual C++ in the Visual Studio 97 timeframe (one revision after first seen in Visual Basic). Because it was based on the introspection capabilities of COM, the Visual Basic versions of IntelliSense were always more robust and complete than the 5.0 and 6.0 (97 and 98 in the Visual Studio naming sequence) versions of Visual C++, which did not have the benefit of being entirely based on COM. These shortcomings (criticized by many VC++ developers since the 97 release) have been largely corrected in the .NET product lines. For example, one of the most requested capabilities missing from the pre-.NET products was support for templates, which is now fully implemented.

IntelliSense has entered a new phase of development with the unified Visual Studio.NET environment first released in 2001, augmented by the more powerful introspection and code documentation capabilities provided by the .NET framework. IntelliSense is now supported by the Visual Studio editors for C++, C#, J#, Visual Basic, XML, HTML and XSLT among others. As of Visual Studio 2005, IntelliSense is now activated by default when the user begins to type, instead of requiring marker characters (though this behavior can be turned off). The IDE has the capability of inferring a greater amount of context based on what the developer is typing, to the point that basic language constructs such as for and while are also included in the choice list. In 2017 Microsoft announced IntelliCode, which uses machine learning to infer exactly which language or library feature is likely to be intended at every keystroke. Initially available as an extension for C# only, it is expected to be built in to future releases of Visual Studio.

Visual Studio 2022 includes artificial-intelligence features, such as GitHub Copilot, which can automatically suggest entire lines of code based on surrounding context.

Other Microsoft products that incorporate IntelliSense include Expression Web, FrontPage 2003, Small Basic, the Visual Basic for Applications IDEs in the Microsoft Office products, Visual Studio Code and many others. SQL Server 2008 Management Studio has autocomplete for the SQL syntax.

Eclipse
The Eclipse IDE has code completion tools that come packaged with the program. It includes notable support for Java, C++, and JavaScript code authoring. The Code Recommenders Eclipse project used to provide powerful intelligent completion, but due to lack of resources, was dropped in Eclipse 2018–12, and then archived in July 2019.

Vim
Vim Intellisense is an advanced code completion system for the Vim editor.

Example
Assume a C++ application being edited in Visual Studio has a class Foo with some member functions:

When the developer references this class in source code, e.g.:

as soon as the user types the period after  , IntelliSense automatically lists all the available member functions (i.e.  and  ) and all the available member attributes (private and protected members can be identified by a padlock picture beside their names). The user can then select one by using the arrow keys and hitting a completion character when the correct member function is highlighted. When available, IntelliSense displays a short description of the member function as given in the source code documentation.

IntelliSense goes further by indicating the required parameters in another pop-up window as the user fills in the parameters. As the user types a variable name, the feature also makes suggestions to complete the variable as they are typed. IntelliSense continues to show parameters, highlighting the pertinent one, as the user types.

The user can "force" IntelliSense to show its pop-up list without context by using or. In Visual Studio this displays the entire application domain object model available to the developer.

title: Code completion


text:
Hermitian adjoint

In mathematics, specifically in operator theory, each linear operator $$ A $$ on an inner product space defines a Hermitian adjoint (or adjoint) operator $$A^*$$ on that space according to the rule

 * $$\langle Ax,y \rangle = \langle x,A^*y \rangle,$$

where $$\langle \cdot,\cdot \rangle$$ is the inner product on the vector space.

The adjoint may also be called the Hermitian conjugate or simply the Hermitian after Charles Hermite. It is often denoted by $A^{†}$ in fields like physics, especially when used in conjunction with bra–ket notation in quantum mechanics. In finite dimensions where operators can be represented by matrices, the Hermitian adjoint is given by the conjugate transpose (also known as the Hermitian transpose).

The above definition of an adjoint operator extends verbatim to bounded linear operators on Hilbert spaces $$H$$. The definition has been further extended to include unbounded densely defined operators, whose domain is topologically dense in, but not necessarily equal to, $$H.$$

Informal definition
Consider a linear map $$A: H_1\to H_2$$ between Hilbert spaces. Without taking care of any details, the adjoint operator is the (in most cases uniquely defined) linear operator $$A^* : H_2 \to H_1$$ fulfilling
 * $$\left\langle A h_1, h_2 \right\rangle_{H_2} = \left\langle h_1, A^* h_2 \right\rangle_{H_1},$$

where $$\langle\cdot, \cdot \rangle_{H_i}$$ is the inner product in the Hilbert space $$H_i$$, which is linear in the first coordinate and conjugate linear in the second coordinate. Note the special case where both Hilbert spaces are identical and $$A$$ is an operator on that Hilbert space.

When one trades the inner product for the dual pairing, one can define the adjoint, also called the transpose, of an operator $$A: E \to F$$, where $$E, F$$ are Banach spaces with corresponding norms $$\|\cdot\|_E, \|\cdot\|_F$$. Here (again not considering any technicalities), its adjoint operator is defined as $$A^*: F^* \to E^*$$ with
 * $$A^*f = f \circ A : u \mapsto f(Au), $$

I.e., $$\left(A^*f\right)(u) = f(Au)$$ for $$f \in F^*, u \in E$$.

The above definition in the Hilbert space setting is really just an application of the Banach space case when one identifies a Hilbert space with its dual. Then it is only natural that we can also obtain the adjoint of an operator $$A: H \to E$$, where $$H$$ is a Hilbert space and $$E$$ is a Banach space. The dual is then defined as $$A^*: E^* \to H$$ with $$A^*f = h_f $$ such that
 * $$\langle h_f, h\rangle_H = f(Ah).$$

Definition for unbounded operators between Banach spaces
Let $$\left(E, \|\cdot\|_E\right), \left(F, \|\cdot\|_F\right)$$ be Banach spaces. Suppose $$ A: D(A) \to F $$ and $$D(A) \subset E$$, and suppose that $$A$$ is a (possibly unbounded) linear operator which is densely defined (i.e., $$D(A)$$ is dense in $$E$$). Then its adjoint operator $$A^*$$ is defined as follows. The domain is
 * $$D\left(A^*\right) := \left\{g \in F^*:~ \exists c \geq 0:~ \mbox{ for all } u \in D(A):~ |g(Au)| \leq c \cdot \|u\|_E\right\}.$$

Now for arbitrary but fixed $$g \in D(A^*)$$ we set $$f: D(A) \to \R$$ with $$f(u) = g(Au)$$. By choice of $$g$$ and definition of $$D(A^*)$$, f is (uniformly) continuous on $$D(A)$$ as $$|f(u)| = |g(Au)| \leq c\cdot \|u\|_E$$. Then by the Hahn–Banach theorem, or alternatively through extension by continuity, this yields an extension of $$f$$, called $$\hat{f}$$, defined on all of $$E$$. This technicality is necessary to later obtain $$A^*$$ as an operator $$D\left(A^*\right) \to E^*$$ instead of $$D\left(A^*\right) \to (D(A))^*.$$ Remark also that this does not mean that $$A$$ can be extended on all of $$E$$ but the extension only worked for specific elements $$g \in D\left(A^*\right)$$.

Now, we can define the adjoint of $$A$$ as
 * $$\begin{align}

A^*: F^* \supset D(A^*) &\to E^* \\ g &\mapsto A^*g = \hat f. \end{align}$$

The fundamental defining identity is thus

 * $$g(Au) = \left(A^* g\right)(u)$$ for $$u \in D(A).$$

Definition for bounded operators between Hilbert spaces
Suppose $H$ is a complex Hilbert space, with inner product $$\langle\cdot,\cdot\rangle$$. Consider a continuous linear operator $A : H → H$ (for linear operators, continuity is equivalent to being a bounded operator). Then the adjoint of $A$ is the continuous linear operator $A^{∗} : H → H$ satisfying

 * $$\langle Ax, y \rangle = \left\langle x , A^* y\right\rangle \quad \mbox{for all } x, y \in H.$$

Existence and uniqueness of this operator follows from the Riesz representation theorem.

This can be seen as a generalization of the adjoint matrix of a square matrix which has a similar property involving the standard complex inner product.

Properties
The following properties of the Hermitian adjoint of bounded operators are immediate:
 * 1) Involutivity: $A^{∗∗} = A$
 * 2) If $A$ is invertible, then so is $A^{∗}$, with $\left(A^*\right)^{-1} = \left(A^{-1}\right)^*$
 * 3) Conjugate linearity:
 * 4) * $(A + B)^{∗} = A^{∗} + B^{∗}$, where $(λA)^{∗} = \overline{λ}A^{∗}$ denotes the complex conjugate of the complex number $\overline{λ}$
 * 5) "Anti-distributivity": $λ$
 * 1) "Anti-distributivity": $(AB)^{∗} = B^{∗}A^{∗}$

If we define the operator norm of $A$ by
 * $$\| A \|_\text{op} := \sup \left\{\|Ax\| : \|x\| \le 1\right\}$$

then
 * $$\left\|A^* \right\|_\text{op} = \|A\|_\text{op}.$$

Moreover,
 * $$\left\|A^* A \right\|_\text{op} = \|A\|_\text{op}^2.$$

One says that a norm that satisfies this condition behaves like a "largest value", extrapolating from the case of self-adjoint operators.

The set of bounded linear operators on a complex Hilbert space $H$ together with the adjoint operation and the operator norm form the prototype of a C*-algebra.

Definition
Let the inner product $$\langle \cdot, \cdot \rangle$$ be linear in the first argument. A densely defined operator $A$ from a complex Hilbert space $H$ to itself is a linear operator whose domain $D(A)$ is a dense linear subspace of $H$ and whose values lie in $H$. By definition, the domain $D(A^{∗})$ of its adjoint $A^{∗}$ is the set of all $y ∈ H$ for which there is a $z ∈ H$ satisfying
 * $$ \langle Ax, y \rangle = \langle x , z \rangle \quad \mbox{for all } x \in D(A).$$

Owing to the density of $$D(A)$$ and Riesz representation theorem, $$z$$ is uniquely defined, and, by definition, $$A^*y=z.$$

Properties 1.–5. hold with appropriate clauses about domains and codomains. For instance, the last property now states that $(AB)^{∗}$ is an extension of $B^{∗}A^{∗}$ if $A$, $B$ and $AB$ are densely defined operators.

ker A$$=(im A)$⊥$
For every $$y \in \ker A^*,$$ the linear functional $$x \mapsto \langle Ax,y \rangle = \langle x,A^*y\rangle $$ is identically zero, and hence $$ y \in (\operatorname{im} A)^\perp.$$

Conversely, the assumption that $$ y \in (\operatorname{im} A)^\perp$$ causes the functional $$x \mapsto \langle Ax,y \rangle$$ to be identically zero. Since the functional is obviously bounded, the definition of $$A^*$$ assures that $$ y \in D(A^*).$$ The fact that, for every $$ x \in D(A),$$ $$\langle Ax,y \rangle = \langle x,A^*y\rangle = 0$$ shows that $$ A^* y \in D(A)^\perp =\overline{D(A)}^\perp = \{0\}, $$ given that $$D(A)$$ is dense.

This property shows that $$\operatorname{ker}A^*$$ is a topologically closed subspace even when $$D(A^*)$$ is not.

Geometric interpretation
If $$H_1$$ and $$H_2$$ are Hilbert spaces, then $$H_1 \oplus H_2$$ is a Hilbert space with the inner product

 * $$\bigl \langle (a,b),(c,d) \bigr \rangle_{H_1 \oplus H_2} \stackrel{\text{def}}{=} \langle a,c \rangle_{H_1} + \langle b,d \rangle_{H_2}, $$

where $$a,c \in H_1$$ and $$b,d \in H_2.$$

Let $$J\colon H\oplus H \to H \oplus H$$ be the symplectic mapping, i.e. $$J(\xi, \eta) = (-\eta, \xi).$$ Then the graph
 * $$G(A^*) =\{(x,y) \mid x\in D(A^*),\ y=A^*x\} \subseteq H \oplus H $$

of $$ A^* $$ is the orthogonal complement of $$JG(A):$$
 * $$G(A^*) = (JG(A))^\perp = \{ (x, y) \in H \oplus H : \bigl \langle (x, y), (-A\xi, \xi) \bigr \rangle_{H \oplus H} = 0\;\;\forall \xi \in D(A)\}. $$

The assertion follows from the equivalences

 * $$ \bigl \langle (x, y), (-A\xi, \xi) \bigr \rangle = 0 \quad \Leftrightarrow \quad \langle A\xi, x \rangle = \langle \xi, y \rangle, $$

and

 * $$\Bigl[ \forall \xi \in D(A)\ \ \langle A\xi, x \rangle = \langle \xi, y \rangle \Bigr] \quad \Leftrightarrow \quad x \in D(A^*)\ \&\ y = A^*x. $$

A$$ is closed
An operator $$A$$ is closed if the graph $$G(A)$$ is topologically closed in $$H \oplus H.$$ The graph $$G(A^*)$$ of the adjoint operator $$A^*$$ is the orthogonal complement of a subspace, and therefore is closed.

A$$ is densely defined ⇔ A is closable
An operator $$A$$ is closable if the topological closure $$G^\text{cl}(A) \subseteq H \oplus H $$ of the graph $$G(A)$$ is the graph of a function. Since $$G^\text{cl}(A)$$ is a (closed) linear subspace, the word "function" may be replaced with "linear operator". For the same reason, $$A$$ is closable if and only if $$(0,v) \notin G^\text{cl}(A)$$ unless $$v=0.$$

The adjoint $$ A^* $$ is densely defined if and only if $$A$$ is closable. This follows from the fact that, for every $$v \in H,$$

 * $$v \in D(A^*)^\perp\ \Leftrightarrow\ (0,v) \in G^\text{cl}(A),$$

which, in turn, is proven through the following chain of equivalencies:

\begin{align} v \in D(A^*)^\perp &\Longleftrightarrow (v,0) \in G(A^*)^\perp \Longleftrightarrow (v,0) \in (JG(A))^\text{cl} = JG^\text{cl}(A) \\ &\Longleftrightarrow (0,-v) = J^{-1}(v,0) \in G^\text{cl}(A) \\ &\Longleftrightarrow (0,v) \in G^\text{cl}(A). \end{align} $$

A$$ = A$cl$
The closure $$ A^\text{cl} $$ of an operator $$A$$ is the operator whose graph is $$ G^\text{cl}(A) $$ if this graph represents a function. As above, the word "function" may be replaced with "operator". Furthermore, $$ A^{**} = A^{\text{cl}},$$ meaning that $$ G(A^{**}) = G^{\text{cl}}(A). $$

To prove this, observe that $$J^* = -J,$$ i.e. $$ \langle Jx,y\rangle_{H \oplus H} = -\langle x,Jy\rangle_{H \oplus H},$$ for every $$x,y \in H \oplus H.$$ Indeed,

\begin{align} \langle J(x_1,x_2),(y_1,y_2)\rangle_{H \oplus H} &= \langle (-x_2,x_1),(y_1,y_2)\rangle_{H \oplus H} = \langle -x_2,y_1\rangle_H + \langle x_1,y_2 \rangle_H \\ &= \langle x_1,y_2 \rangle_H + \langle x_2,-y_1 \rangle_H = \langle (x_1,x_2),-J(y_1,y_2)\rangle_{H \oplus H}. \end{align} $$ In particular, for every $$y \in H \oplus H$$ and every subspace $$ V \subseteq H \oplus H,$$ $$y \in (JV)^\perp$$ if and only if $$Jy \in V^\perp.$$ Thus, $$ J[(JV)^\perp] = V^\perp $$ and $$ [J[(JV)^\perp]]^\perp = V^\text{cl}.$$ Substituting $$ V = G(A),$$ obtain $$ G^\text{cl}(A) = G(A^{**}).$$

A$$ = (A$cl$)$$
For a closable operator $$A,$$ $$ A^* = \left(A^\text{cl}\right)^*, $$ meaning that $$G(A^*) = G\left(\left(A^\text{cl}\right)^*\right).$$ Indeed,

G\left(\left(A^\text{cl}\right)^*\right) = \left(JG^\text{cl}(A)\right)^\perp = \left(\left(JG(A)\right)^\text{cl}\right)^\perp = (JG(A))^\perp = G(A^*). $$

Counterexample where the adjoint is not densely defined
Let $$H=L^2(\mathbb{R},l),$$ where $$l$$ is the linear measure. Select a measurable, bounded, non-identically zero function $$f \notin L^2,$$ and pick $$\varphi_0 \in L^2 \setminus \{0\}.$$ Define

 * $$A \varphi = \langle f,\varphi\rangle \varphi_0.$$

It follows that $$D(A) = \{\varphi \in L^2 \mid \langle f,\varphi\rangle \neq \infty\}.$$ The subspace $$D(A)$$ contains all the $$L^2$$ functions with compact support. Since $$\mathbf{1}_{[-n,n]} \cdot \varphi\ \stackrel{L^2}{\to}\ \varphi,$$ $$A$$ is densely defined. For every $$\varphi \in D(A)$$ and $$\psi \in D(A^*),$$

 * $$\langle \varphi, A^*\psi \rangle = \langle A\varphi, \psi \rangle = \langle \langle f,\varphi \rangle\varphi_0, \psi \rangle = \langle f,\varphi \rangle\cdot \langle \varphi_0, \psi \rangle = \langle \varphi, \langle \varphi_0, \psi \rangle f\rangle. $$

Thus, $$A^* \psi = \langle \varphi_0, \psi \rangle f.$$ The definition of adjoint operator requires that $$\mathop{\text{Im}}A^* \subseteq H=L^2.$$ Since $$f \notin L^2,$$ this is only possible if $$\langle \varphi_0, \psi \rangle= 0.$$ For this reason, $$D(A^*) = \{\varphi_0\}^\perp.$$ Hence, $$A^*$$ is not densely defined and is identically zero on $$D(A^*).$$ As a result, $$A$$ is not closable and has no second adjoint $$A^{**}.$$

Hermitian operators
A bounded operator $A : H → H$ is called Hermitian or self-adjoint if
 * $$A = A^*$$

which is equivalent to
 * $$\langle Ax, y \rangle = \langle x , A y \rangle \mbox{ for all } x, y \in H.$$

In some sense, these operators play the role of the real numbers (being equal to their own "complex conjugate") and form a real vector space. They serve as the model of real-valued observables in quantum mechanics. See the article on self-adjoint operators for a full treatment.

Adjoints of conjugate-linear operators
For a conjugate-linear operator the definition of adjoint needs to be adjusted in order to compensate for the complex conjugation. An adjoint operator of the conjugate-linear operator $A$ on a complex Hilbert space $H$ is an conjugate-linear operator $A^{∗} : H → H$ with the property:

 * $$\langle Ax, y \rangle = \overline{\left\langle x , A^* y \right\rangle} \quad \text{for all } x, y \in H.$$

Other adjoints
The equation
 * $$\langle Ax, y \rangle = \left\langle x, A^* y \right\rangle$$

is formally similar to the defining properties of pairs of adjoint functors in category theory, and this is where adjoint functors got their name from.

title: Hermitian adjoint


text:
Typing

Typing is the process of writing or inputting text by pressing keys on a typewriter, computer keyboard, mobile phone, or calculator. It can be distinguished from other means of text input, such as handwriting and speech recognition. Text can be in the form of letters, numbers and other symbols. The world's first typist was Lillian Sholes from Wisconsin in the United States, the daughter of Christopher Sholes, who invented the first practical typewriter.

User interface features such as spell checker and autocomplete serve to facilitate and speed up typing and to prevent or correct errors the typist may make.

Hunt and peck
Hunt and peck (two-fingered typing) is a common form of typing in which the typist presses each key individually. Instead of relying on the memorized position of keys, the typist must find each key by sight. Although good accuracy may be achieved, the use of this method may also prevent the typist from being able to see what has been typed without glancing away from the keys, and any typing errors that are made may not be noticed immediately. Due to the fact that only a few fingers are used in this technique, this also means that the fingers are forced to move a much greater distance.

Touch typing

In this technique, the typist keeps their eyes on the source copy at all times. Touch typing also involves the use of the home row method, where typists rest their wrist down, rather than lifting up and typing (which can cause carpal tunnel syndrome ). To avoid this, typists should sit up tall, leaning slightly forward from the waist, place their feet flat on the floor in front of them with one foot slightly in front of the other, and keep their elbows close to their sides with forearms slanted slightly upward to the keyboard; fingers should be curved slightly and rest on the home row.

Many touch typists also use keyboard shortcuts when typing on a computer. This allows them to edit their document without having to take their hands off the keyboard to use a mouse. An example of a keyboard shortcut is pressing the key plus the S key to save a document as they type, or the Ctrl key plus the Z key to undo a mistake. Other shortcuts are the key plus the  to copy and the  key and the  key to paste, and the  key and the  key to cut. Many experienced typists can feel or sense when they have made an error and can hit the key and make the correction with no increase in time between keystrokes.

Hybrid
There are many idiosyncratic typing styles in between novice-style "hunt and peck" and touch typing. For example, many "hunt and peck" typists have the keyboard layout memorized and are able to type while focusing their gaze on the screen. Some use just two fingers, while others use 3–6 fingers. Some use their fingers very consistently, with the same finger being used to type the same character every time, while others vary the way they use their fingers.

One study examining 30 subjects, of varying different styles and expertise, has found minimal difference in typing speed between touch typists and self-taught hybrid typists. According to the study, "The number of fingers does not determine typing speed... People using self-taught typing strategies were found to be as fast as trained typists... instead of the number of fingers, there are other factors that predict typing speed... fast typists... keep their hands fixed on one position, instead of moving them over the keyboard, and more consistently use the same finger to type a certain letter." To quote Prof. Dr. Anna Feit: "We were surprised to observe that people who took a typing course, performed at similar average speed and accuracy, as those that taught typing to themselves and only used 6 fingers on average."

Thumbing
A late 20th century trend in typing, primarily used with devices with small keyboards (such as PDAs and Smartphones), is thumbing or thumb typing. This can be accomplished using either only one thumb or both the thumbs, with more proficient typists reaching speeds of 100 words per minute. Similar to desktop keyboards and input devices, if a user overuses keys which need hard presses and/or have small and unergonomic layouts, it could cause thumb tendonitis or other repetitive strain injury.

Words per minute
Words per minute (WPM) is a measure of typing speed, commonly used in recruitment. For the purposes of WPM measurement a word is standardized to five characters or keystrokes. Therefore, "brown" counts as one word, but "mozzarella" counts as two.

The benefits of a standardized measurement of input speed are that it enables comparison across language and hardware boundaries. The speed of an Afrikaans-speaking operator in Cape Town can be compared with a French-speaking operator in Paris.

Today, even Written Chinese can be typed very quickly using the combination of a software prediction system and by typing their sounds in Pinyin. Such prediction software even allows typing short-hand forms while producing complete characters. For example, the phrase "nǐ chī le ma" (你吃了吗) meaning "Have you eaten yet?" can be typed with just 4 strokes: "nclm".

Alphanumeric entry
In one study of average computer users, the average rate for transcription was 33 words per minute, and 19 words per minute for composition. In the same study, when the group was divided into "fast", "moderate" and "slow" groups, the average speeds were 40 wpm, 35 wpm, and 23 wpm respectively. An average professional typist reaches 50 to 80 wpm, while some positions can require 80 to 95 wpm (usually the minimum required for dispatch positions and other typing jobs), and some advanced typists work at speeds above 120 wpm. Two-finger typists, sometimes also referred to as "hunt and peck" typists, commonly reach sustained speeds of about 37 wpm for memorized text and 27 wpm when copying text, but in bursts may be able to reach speeds of 60 to 70 wpm. From the 1920s through the 1970s, typing speed (along with shorthand speed) was an important secretarial qualification and typing contests were popular and often publicized by typewriter companies as promotional tools.

A less common measure of the speed of a typist, CPM is used to identify the number of characters typed per minute. This is a common measurement for typing programs, or typing tutors, as it can give a more accurate measure of a person's typing speed without having to type for a prolonged period of time. The common conversion factor between WPM and CPM is 5. It is also used occasionally for associating the speed of a reader with the amount they have read. CPM has also been applied to 20th century printers, but modern faster printers more commonly use PPM (pages per minute).

The fastest typing speed ever, 216 words per minute, was achieved by Stella Pajunas-Garnand from Chicago in 1946 in one minute on an IBM electric   using the QWERTY keyboard layout. , writer Barbara Blackburn was the fastest English language typist in the world, according to The Guinness Book of World Records. Using the Dvorak keyboard layout, she had maintained 150 wpm for 50 minutes, and 170 wpm for shorter periods, with a peak speed of 212 wpm. Barbara Blackburn, who failed her QWERTY typing class in high school, first encountered the Dvorak layout in 1938 and then she quickly learned to achieve very high speeds of typing, also she occasionally toured giving speed-typing demonstrations during her secretarial career. She appeared on Late Night with David Letterman on January 24, 1985, but felt that Letterman made a spectacle of her.

The recent emergence of several competitive typing websites has allowed fast typists on computer keyboards to emerge along with new records, though many of these are unverifiable. Some notable, verified records include 255 wpm on a one-minute, random-word test by a user under the username slekap and occasionally bailey, 213 wpm on a 1-hour, random-word test by Joshua Hu, 221 wpm average on 10 random quotes by Joshua Hu, and first place in the 2020 Ultimate Typing Championship by Anthony Ermollin based on an average of 180.88 wpm on texts of various lengths. These three people are the most commonly cited fastest typists in online typing communities. All of their records were set on the QWERTY keyboard layout.

Using a personalized interface, physicist Stephen Hawking, who suffered from amyotrophic lateral sclerosis, managed to type 15 wpm with a switch and adapted software created by Walt Woltosz. Due to a slowdown of his motor skills, his interface was upgraded with an infrared camera that detected "twitches in the cheek muscle under the eye." His typing speed decreased to approximately one word per minute in the later part of his life.

Numeric entry
The numeric entry, or 10-key, speed is a measure of one's ability to manipulate a numeric keypad. Generally, it is measured in keystrokes per hour (KPH).

Error analysis
With the introduction of computers and word-processors, there has been a change in how text-entry is performed. In the past, using a typewriter, speed was measured with a stopwatch and errors were tallied by hand. With the current technology, document preparation is more about using word-processors as a composition aid, changing the meaning of error rate and how it is measured. Research performed by R. William Soukoreff and I. Scott MacKenzie, has led to a discovery of the application of a well-known algorithm. Through the use of this algorithm and accompanying analysis technique, two statistics were used, minimum string distance error rate (MSD error rate) and keystrokes per character (KSPC). The two advantages of this technique include:

 * Participants are allowed to enter text naturally, since they may commit errors and correct them.
 * The identification of errors and generation of error rate statistics is easy to automate.

Deconstructing the text input process
Through analysis of keystrokes, the keystrokes of the input stream were divided into four classes: Correct (C), Incorrect Fixed (IF), Fixes (F), and Incorrect Not Fixed (INF). These key stroke classification are broken down into the following

 * The two classes Correct and Incorrect Not Fixed comprise all of the characters in transcribed text.
 * Fixes (F) keystrokes are easy to identify, and include keystrokes such as backspace, delete, cursor movements, and modifier keys.
 * Incorrect Fixed (IF) keystrokes are found in the input stream, but not the transcribed text, and are not editing keys.

Using these classes, the Minimum String Distance Error Rate and the Key Strokes per Character statistics can both be calculated.

Minimum string distance error rate
The minimum string distance (MSD) is the number of "primitives" which is the number of insertions, deletions, or substitutions to transform one string into another. The following equation was found for the MSD Error Rate.

MSD Error Rate = $$(INF/(C + INF)) * 100\%$$

Key strokes per character (KSPC)
With the minimum string distance error, errors that are corrected do not appear in the transcribed text. The following example shows why this can be an important class of errors to consider:

Presented Text:      the quick brown

Input Stream:        the quix<-ck brown

Transcribed Text:    the quick brown

In the above example, the incorrect character ('x') was deleted with a backspace ('<-'). Since these errors do not appear in the transcribed text, the MSD error rate is 0%. That is the purpose of the key strokes per character (KSPC) statistic.

KSPC = $$(C+INF+IF+F)/(C+INF)$$

There are some shortcomings of the KSPC statistic, such as:

 * High KSPC values can be related to either many errors which were corrected, or few errors which were not corrected; however, there is no way to distinguish the two.
 * KSPC depends on the text input method, and cannot be used to meaningfully compare two different input methods, such as a QWERTY keyboard and a multi-tap device.
 * There is no obvious way to combine KSPC and MSD into an overall error rate, even though they have an inverse relationship.

Further metrics
Using the classes described above, further metrics were defined by R. William Soukoreff and I.Scott MacKenzie:

Error correction efficiency refers to the ease with which the participant performed error correction. Participant conscientiousness is the ratio of corrected errors to the total number of error, which helps distinguish perfectionists from apathetic participants. If C represents the amount of useful information transferred, INF, IF, and F represent the proportion of bandwidth wasted.
 * Correction Efficiency = IF/F
 * Participant Conscientiousness = IF / (IF + INF)
 * Utilized Bandwidth = C / (C + INF + IF + F)
 * Wasted Bandwidth = (INF + IF + F)/ (C + INF + IF + F)

Total error rate
The classes described also provide an intuitive definition of total error rate:

 * Total Error Rate = ((INF + IF)/ (C + INF + IF)) * 100%
 * Not Corrected Error Rate = (INF/ (C + INF + IF)) * 100%
 * Corrected Error Rate = (IF/ (C + INF + IF)) * 100%

Since these three error rates are ratios, they are comparable between different devices, something that cannot be done with the KSPC statistic, which is device dependent.

Tools for text entry research
Currently, two tools are publicly available for text entry researchers to record text entry performance metrics. The first is TEMA that runs only on the Android (operating system). The second is WebTEM that runs on any device with a modern Web browser, and works with almost all text entry technique.

Keystroke dynamics
Keystroke dynamics, or typing dynamics, is the obtaining of detailed timing information that describes exactly when each key was pressed and when it was released as a person is typing at a computer keyboard for biometric identification, similar to speaker recognition. Data needed to analyze keystroke dynamics is obtained by keystroke logging.

The behavioral biometric of Keystroke Dynamics uses the manner and rhythm in which an individual types characters on a keyboard or keypad.

title: Typing


text:
European Banking Federation

The European Banking Federation (EBF) is a trade association representing national banking associations in countries of the European Union and the European Free Trade Association. It represents over 3,500 banks and about 2.6 million employees. It was established in 1960 as the Fédération bancaire européenne.

Members
, the EBF's members were:
 * Austria - Verband österreichischer Banken und Bankiers (Bankenverband)
 * Belgium - Febelfin
 * Bulgaria - Асоциация на банките в България / Association of Banks in Bulgaria (ABB)
 * Croatia - Hrvatska udruga banaka / Croatian Banking Association (HUB)
 * Cyprus - Association of Cyprus Banks (ACB)
 * Czech Republic - Czech Banking Association (CBA)
 * Denmark - Finance Denmark
 * Estonia - Estonian Banking Association
 * Finland - Finance Finland
 * France - Fédération Bancaire Française (FBF)
 * Germany - Bundesverband deutscher Banken (BdB) and Association of German Public Banks (VÖB)
 * Greece - Ελληνική Ένωση Τραπεζών / Hellenic Bank Association (HBA)
 * Hungary - Hungarian Banking Association
 * Iceland - Samtök fjármálafyrirtækja (SFF)
 * Ireland - Banking and Payments Federation Ireland
 * Italy - Associazione Bancaria Italiana (ABI)
 * Latvia - Finance Latvia Association
 * Liechtenstein - Liechtensteinische Bankenverband / Liechtenstein Bankers Association
 * Lithuania - Lietuvos Bankų Asociacija / Lithuanian Banking Association (LBA)
 * Luxembourg - Association des Banques et Banquiers Luxembourg (ABBL)
 * Malta - Malta Bankers' Association (MBA)
 * Netherlands - Dutch Banking Association
 * Norway - Finance Norway
 * Poland - Związek Banków Polskich (ZBP)
 * Portugal - Associação Portuguesa de Bancos (APB)
 * Romania - Romanian Association of Banks (ARB)
 * Slovakia - Slovak Banking Association (SBA)
 * Slovenia - Združenje bank Slovenije / The Bank Association of Slovenia
 * Spain - Asociación Española de Banca (AEB)
 * Sweden - Swedish Bankers' Association
 * Switzerland - Swiss Bankers Association
 * United Kingdom - UK Finance

At the same date, ten countries had associate status: Albania, Andorra, Armenia, Bosnia and Herzegovina, North Macedonia, Moldova, Monaco, Montenegro, Serbia and Turkey.

title: European Banking Federation


text:
Phile

Phile or Philes may refer to:

 * -phile, a suffix in the English language, derived from the Greek philia
 * Phile (politician), a magistrate in Ancient Greece
 * Phile, a misspelling of computer file, seen in BBS hacker culture
 * Alexios Philes, Byzantine general
 * Manuel Philes, Byzantine poet
 * Theodore Philes, Byzantine governor

title: Phile


text:
Adobe Fireworks

Adobe Fireworks (formerly Macromedia Fireworks) was a bitmap and vector graphics editor, which Adobe acquired in 2005. Fireworks was made for web designers for rapidly creating website prototypes and application interfaces. Its features included slices, which are segments of an image that are converted to HTML elements, and the ability to add hotspots, which are segments of an image that are converted to hyperlinks. It was designed to integrate with other Adobe products such as Adobe Dreamweaver and Adobe Flash. It was available as either a standalone product or bundled with Adobe Creative Suite. Older versions were bundled with Macromedia Studio. Adobe discontinued Fireworks in 2013, citing the increasing overlap in functionality with its other products such as Adobe Photoshop, Adobe Illustrator, and Adobe Edge.

User interface
Fireworks' user interface is consistent with the rest of Adobe Creative Suite, similar to that of Adobe Photoshop. On macOS, it is possible to display the application in multiple document interface mode or the standard viewing mode where all toolbars float freely on the screen.

Hierarchical layers
All the layers can be accessed from the Layers panel. Layers may be wider or taller than the image itself. However, the final image is produced by hiding those areas that exit the image boundary.

Smart guides
Fireworks support guides, horizontal or vertical lines that act like a real-world ruler to help drawing, content placement and image composition. A user may place one or more guides on the image at any time and use it as a visual aid. For instance a guide is useful when a piece of text must be placed in line with another graphical item. Additionally, the user may enable the snap feature of the Fireworks, which causes objects (pieces of image, text or layers) drag to the vicinity of a guide to snap to it.

The smart guides however, are not placed by users. They are areas of the image that may interest the user such as the image boundaries, middle of the image or general boundaries of another object. When a user drags an object, Fireworks tries to guess what the user intends to do with the object and draws temporary visual and placement aids. This feature was added with the release of CS4.

Symbols
Reusable elements can be designated as symbols and placed at multiple pages or on the same page. When the master symbol is edited, Fireworks propagates the change to all instances of that symbol.

9-slice scaling
This feature ensures that rounded rectangles maintain their roundness when transformed depending on where the guides are placed. CS4 has this feature exposed as a tool. With this feature introduced in the CS3 version, its usage was limited to symbols.

Image optimization
Fireworks were created specifically for web production. Since not every user may be in possession of a fast Internet connection, it is in the best interest of the web developers to optimize the size of their digital contents. In terms of image compression, Fireworks has a better compression rate than Photoshop with JPEG, PNG and GIF images.

Adobe Creative Suite integration
Fireworks understands the Adobe Photoshop and Adobe Illustrator file formats ( and   files) as well as Encapsulated PostScript format (  files).

Export
Fireworks can export images to multiple file formats including PNG, JPEG, GIF, Animated GIF, TIFF, SWF, BMP, WBMP and PDF. It can also export to SVG (with the help of a free Export extension ) and FXG 2.0. Fireworks can export to HTML by converting slices to HTML elements.

States
Previously known as frames, states are used for animation purposes. They are also used for defining behaviors in cases of symbol buttons like Up, Down, Over (changing the visual style of buttons on click, release, and hover with the mouse).

Version history

 * 1998: Macromedia Fireworks
 * 1999: Macromedia Fireworks 2
 * 2000: Macromedia Fireworks 3
 * 2001: Macromedia Fireworks 4
 * 2002: Macromedia Fireworks MX (v6.0)
 * 2003: Macromedia Fireworks MX 2004 (v7.0)
 * 2005: Macromedia Fireworks 8
 * 2007: Adobe Fireworks CS3 (v9.0)
 * 2008: Adobe Fireworks CS4 (v10.0)
 * 2010: Adobe Fireworks CS5 (v11.0)
 * 2011: Adobe Fireworks CS5.1 (v11.1)
 * 2012: Adobe Fireworks CS6 (v12.0)

title: Adobe Fireworks


text:
John Markoff

John Gregory Markoff (born October 24, 1949 ) is a journalist best known for his work covering technology at The New York Times for 28 years until his retirement in 2016, and a book and series of articles about the 1990s pursuit and capture of hacker Kevin Mitnick.

Biography
Markoff was born in Oakland, California, and grew up in Palo Alto, California. He graduated from Whitman College, Walla Walla, Washington, with a B.A. in sociology in 1971. Additionally he received an M.A. in sociology from the University of Oregon in 1976.

After leaving graduate school, he returned to California where he began writing for Pacific News Service, an alternative news syndicate based in San Francisco. He freelanced for a number of publications including The Nation, Mother Jones and Saturday Review. In 1981 he became part of the original staff of the computer industry weekly InfoWorld. In 1984 he became an editor at Byte Magazine and in 1985 he left to become a reporter in the business section of the San Francisco Examiner, where he wrote about Silicon Valley.

In 1988 he moved to New York to write for the business section of the New York Times. In November 1988 he reported that Robert Tappan Morris, son of National Security Agency cryptographer Robert Morris, was the author of what would become known as the Internet worm.

In December 1993 he wrote an early article about the World Wide Web, referring to it as a "map to the buried treasures of the Information Age."

Markoff and Kevin Mitnick

On July 4, 1994, he wrote an article about Kevin Mitnick, who was then a fugitive from a number of law enforcement agencies. He wrote several more pieces detailing Mitnick's capture. Markoff also co-wrote, with Tsutomu Shimomura, the book Takedown: The Pursuit and Capture of America's Most Wanted Computer Outlaw about the chase.

Markoff's writing about Mitnick was the subject of criticism by Mitnick supporters and unaffiliated parties who maintained that Markoff's accounts exaggerated or even invented Mitnick's activities and successes. Markoff was also accused by Jonathan Littman of journalistic impropriety and of over-hyping Mitnick's actual crimes. Littman published a more sympathetic account of Mitnick's time as a fugitive in his own book on the incident, The Fugitive Game. Markoff stood by his reporting.

The book later became a film that was released direct to video in the United States. The film went much further, with Markoff himself stating to the San Francisco Chronicle in 2000, "I thought it was a fundamentally dishonest movie." Mitnick stated that he settled a lawsuit with distributor Miramax over the film for an undisclosed sum.

Post-Mitnick
After Mitnick, Markoff continued to write about technology, focusing at times on wireless networking, writing early stories about non-line-of-sight broadband wireless, phased-array antennas, and multiple-in, multiple-out (MIMO) antenna systems to enhance Wi-Fi. He covered Jim Gillogly's 1999 break of the first three sections of the CIA's Kryptos cipher, and writes regularly about semiconductors and supercomputers as well. He wrote the first two articles describing Admiral John Poindexter's return to government and the creation of the Total Information Awareness project. He shared the 2005 Gerald Loeb Award in the Deadline Writing category for the story "End of an Era". In 2009 he moved from the Business/Tech section of the New York Times to the Science section.

Markoff contributed to the New York Times staff entry that received the 2013 Pulitzer Prize for Explanatory Reporting. The series of 10 articles explored the business practices of Apple and other technology companies. He retired from his full-time position with The New York Times on December 1, 2016. He continues to work as a freelance journalist for the Times and other organizations and volunteers at the Computer History Museum. He is an affiliated fellow of the Stanford Institute for Human-Centered Artificial Intelligence.

Markoff is interviewed in Do You Trust This Computer?, a 2018 documentary on artificial intelligence.

Books

 * The High Cost of High Tech (with Lennie Siegel) (1985) ISBN 0-06-039045-X
 * Takedown: The Pursuit and Capture of America's Most Wanted Computer Outlaw (with Tsutomu Shimomura) (1995) ISBN 0-7868-6210-6
 * What the Dormouse Said: How the 60s Counterculture Shaped the Personal Computer Industry (2005) ISBN 0-670-03382-0
 * Machines of Loving Grace: The Quest for Common Ground Between Humans and Robots (2015)
 * Whole Earth: The Many Lives of Stewart Brand (Penguin Press, 2022). ISBN 0735223947
 * Machines of Loving Grace: The Quest for Common Ground Between Humans and Robots (2015)
 * Whole Earth: The Many Lives of Stewart Brand (Penguin Press, 2022). ISBN 0735223947
 * Whole Earth: The Many Lives of Stewart Brand (Penguin Press, 2022). ISBN 0735223947

title: John Markoff


text:
Command history

Command history is a feature in many operating system shells, computer algebra programs, and other software that allows the user to recall, edit and rerun previous commands.

Command line history was added to Unix in Bill Joy's C shell of 1978; Joy took inspiration from an earlier implementation in Interlisp. It quickly became popular because it made the C shell fast and easy to use. History has since become a standard feature in other shells, including ksh, Bash and Microsoft's cmd.exe. History addressed two important scenarios:

 * 1) Executing the same command or a short sequence of commands over and over.  An example might be a developer frequently compiling and running a program.
 * 2) Correcting mistakes or rerunning a command with only a small modification.

In Joy's original C shell, the user could refer to a previous command by typing an exclamation,, followed by additional characters to specify a particular command, only certain words, or to edit it in some way before pasting it back into the command line. For example:

 * meant the entire previous command.
 * meant just the last word of the previous command.
 * meant the command that started with abc.

The usual implementation today is to combine history with command-line editing. The cursor keys are used to navigate up and down through the history list and left or right to anyplace on the line, where the user can simply type a desired change. But some implementations are menu-based: The user presses a certain function key which displays a menu of recent commands, which the user can select one by typing a number.

Some implementation such as Bash support to record command history to a file ( command).

title: Command history


text:
William Beckwith McInnes

William Beckwith McInnes (18 May 1889 – 9 November 1939) was an Australian portrait painter, winner of the Archibald Prize seven times for his traditional style paintings. He was acting-director at the National Gallery of Victoria and an instructor in its art school.

Early life
McInnes was born in St Kilda, a suburb of Melbourne, to Malcolm McInnes and his wife Alice Agnes, née Beckwith. Despite lack of family artistic tradition, he was keen to draw from the time he could hold a pencil. In 1903, at 14 years of age, he enrolled in the drawing school of the National Gallery of Victoria under Frederick McCubbin. Later he moved up to the painting school under Lindsay Bernard Hall.

Artistic career
He won his first prizes for drawing the figure from life, and for painting a head from life, and shared the prize for a landscape in 1908.

Soon afterwards McInnes held a successful show of his paintings at the Melbourne Athenaeum Gallery in conjunction with F. R. Crozier, which was followed in 1911 by a journey to Europe where he did much landscape painting and made acquaintance with the masterpieces of Rembrandt, Velasquez and Raeburn.

McInnes was represented in London at the exhibition of the Royal Institute of Painters in oils in 1913.

He returned to Melbourne in the same year, where a one-man show was held at the Athenaeum gallery and nearly everything was sold. In 1916 he acted as locum tenens for Frederick McCubbin, master of the school of drawing at the National Gallery of Victoria, during McCubbin's six months' leave of absence. McInnes was temporarily appointed to the position in 1918 after McCubbin's death, and in 1920 he was permanently appointed.

In 1921, he won the first Archibald Prizes for portraiture. He went on to win the award a total of seven times.

McInnes revisited Europe in 1925 and found he was in great demand as a portrait painter. For many years he was unable to spare time to do landscape work. In 1927 he was commissioned by the Federal government to depict the opening of the first parliament in Canberra by the Duke of York. In 1928 he exhibited with the Royal Academy, and in 1933 he visited England again to paint the Duke of York (later King George VI).

In the following year when Bernard Hall left for England as adviser for the Felton bequest, McInnes was appointed acting-director of the National Gallery of Victoria, and on Hall's death, was appointed head of the painting school. In 1937 McInnes became an invited foundation member of, and exhibited with, Robert Menzies' anti-modernist organisation, the Australian Academy of Art.

Amongst the many portraits by McInnes were those of the surgeons Archibald Watson and Wood Jones.

McInnes' artwork is featured at the Art Gallery of South Australia and the Art Gallery of NSW. In addition, McInnes has painted a variety of important people in Australian history including officials and aristocratic families.

Late life
McInnes suffered from an imperfect heart all his life. On 30 November 1937 around midnight the car he was driving struck and killed a pedestrian, James Lowrey, on Brunswick Street in Fitzroy. At the inquest evidence was brought forward that a drug (Luminal) he was taking for the condition could have affected his driving and been responsible for his staggering and not remembering details of the accident. He was not convicted of any offence.

His general health became affected and in July 1939 he resigned his position as master of the National Gallery art school. He died on 9 November 1939. He married Violet Muriel Musgrave in 1915, a capable flower painter, who survived him with four sons and two daughters.

McInnes' Archibald Prize winners

 * 1921 - Desbrowe Annear
 * 1922 - Professor Harrison Moore
 * 1923 - Portrait of a Lady
 * 1924 - Miss Collins
 * 1926 - Silk and Lace (Miss Esther Paterson)
 * 1930 - Drum-Major Harry McClelland
 * 1936 - Dr. Julian Smith

McInnes also won the Wynne Prize in 1918 with The Grey Road.

title: William Beckwith McInnes