How's Hegel's conception of Geist different from the bible's conception of the holy spirit?

Question: I was seeing a documentary on Christianity, in it many times the word "Holy spirit" was mentioned with subtext that it was something written in the bible. I had previously heard Hegel came up with a related sounding idea of the >>Heiliger Geist<<. Do these two ideas have any relation to each other? What exactly are the differences?
Comment: See [Geist: Hegel](https://en.wikipedia.org/wiki/Geist#Hegelianism): "*Geist* is a central concept in Hegel's *The Phenomenology of Spirit*. According to Hegel, the *Weltgeist* ("world spirit") is not an actual object or a transcendental, Godlike thing, but a means of philosophizing about history." "Hegel's description of Napoleon as "the world-soul on horseback" (*die Weltseele zu Pferde*) became proverbial. The phrase is a shortened paraphrase of Hegel's words in a letter written in 1806: 'I saw the Emperor – this world-soul – riding out of the city on reconnaissance.' "
Comment: Relevant: https://philosophy.stackexchange.com/questions/14533/what-did-hegel-mean-by-world-spirit
Comment: The Holy Spirit in Christian theology is an aspect of the triune God along with Jesus and the Father (this is trinitarianism, which most Western Christians are. I'm not sure what roll the Holy Spirit plays in unitarianism, but it's probably similar). The Holy Spirit is said to indwell Christians and to be responsible for communicating between God and man and is responsible for prompting the conscience.
Comment: We can hardly assert that Napoleon was an incarnation of Holy spirit...
Answer: First taking a look at the meaning of Holy Spirit.
From Take Our Word For It

Holy Ghost is used interchangeably with Holy Spirit today and is a much older term.  It dates back to Old English, where the form was
hálga gást or hálig gást, composed of two distinct words, as today.  The first record of the term comes from about 900 in Halsuncge in
Durham Ritual: "Ic eow halsige on fæder naman, and on suna naman..and on ðæs halgan gastes."  ...
The etymology of holy, spirit, and ghost are also of interest as
a part of this discussion.   Holy is, as might be expected based on
the etymology of Holy Ghost, an Old English term.   Its form in
about 1000 A.D. was halig and it derives from the Indo-European root
hailo- or kailo- "free from injury, whole", whence comes also English hale as in "hale and hearty".
... spirit was initially used to translate Greek pneuma and Hebrew
ruah, starting in about 1250, and all versions of the Bible from Wyclif onward use spirit in translation of the Greek and Hebrew.
Prior to the Middle Ages, however, ghost was used.   It comes from
the Indo-European root gheis- "fear or amazement", and there are
descendants of that root in most of the Germanic languages, all of
them possessing similar meanings.

From Of Spirit: Heidegger and the Question by J. Derrida, page 98, translating Martin Heidegger

The burning up is the radiance of a reddening  glare.  What burns
itself up is Being-outside-itself  (das Ausser-sich) which illuminates
and makes  shine, which also, however (indessen auch), can  devour
tirelessly and consume everything up to  and including the white of
the ash (in das Weisse  der Asche verzehren kann).
"The flame is the brother of the palest" is what  we read in the poem Verwandlung des Bösen  (Transmutation of the Evil One).  Trakl
envisages  "spirit" on the basis of this essence which is named  in
the originary meaning (in der ursprünglichen  Bedeutung) of the word
"Geist," for gheis means:  to be thrown (aufgebracht), transported [or
transposed, deported: entsetzt, again -- and I  believe this is the
most determining predicate],  outside itself (ausser sich).

So here we have a process like a burning, a shine, a transport outside itself.  What might be interpreted as a shock, out of one's mind (a transport), a gasp (same root), a very much spirited emotional state.  Definitely a lot going on, in a process.
And then we have Hegel taking this idea of process to the scale of the Absolute.
From Nietzsche, Philosopher, Psychologist, Antichrist, page 239

Both [Hegel and Nietzsche] postulated a single basic force whose very
essence is to manifest itself in diverse ways and to create
multiplicity—not ex nihilo, but out of itself.
Hegel found the prototype of such a creative force in the Christian
conception of the Holy Spirit, which he interpreted in his own
characteristic fashion: God the Father must, without any external
compulsion, become incarnate, embody himself, and thus become God the
Son; in the Holy Spirit, however, God the Father and God the Son are
one.  Thus the spirit is a unity that is not an "inert simplicity,"
nor an "unstained self-identity," but essentially a process.
Comment: The quote from Take Our Word For It doesn't add anything to the answer. The etymology of the word tells nothing about the concept.
Comment: My problem with this answer is rather that a secondary source which makes claims about what Hegel might have thought about the holy ghost in relation to father and son is not quite adding something to the difference between the Catholic holy ghost and Hegelian absolute Geist or world spirit.
Comment: @DavidGudeman I guess I'm focusing on the process aspect, as dynamic intelligence or burning life force. The Catholic encyclopedia says the [Holy Ghost](https://www.newadvent.org/cathen/07409a.htm) is a Person, which relates less easily to the idea in the Hegel quote.
Comment: But the question was about the difference between Hegel and the Holy Spirit, so if a quote from the Catholic encyclopedia suggests that the two ideas aren't relatable, that's the answer.
Comment: @DavidGudeman Inasmuch as a person is/has a spirit it make the two ideas relatable.
Comment: Yet you are not answering the question which was asked.
Comment: @DavidGudeman "*Do these two ideas have any relation to each other?*" - They relate insofar as they are both characterised as activity/process, agency.
Comment: 99% of the things that people talk about are characterized by activity-/process, agency. I don't know anything about Hegel, but if you need to suppress the personhood of the Holy Spirit to draw a similarity, you are stretching the point beyond breaking. It's like someone asking how Aristotle is related to karma and you make some stretched point that makes no sense to anyone who knows that Aristotle is a person, not a principle.
Comment: From [Wikipedia](https://en.wikipedia.org/wiki/Trinity#Holy_Spirit_in_the_New_Testament) : "*another argument from the Cappadocian Fathers ... reasoned that ... the Holy Spirit has the same relationship to God as the spirit within us has to us.*" - which supports the endeavour to analyse what 'spirit' means in general.
Comment: The Holy Spirit is briefly discussed here : [In Our Time - The Nicene Creed](https://www.bbc.co.uk/sounds/play/b008jglt) at 36 minutes in.  Significant emphasis on 'mystery'.


Max-turn hamiltonian path in square grids

Question: Given an $n \times n$ square grid graph, what is the maximum number of turns a Hamiltonian path can take?
Comment: The same question would seem to be of interest for a Hamiltonian circuit.
Answer: Answer to OP's question (proof follows):
For Hamitlonian paths: if $n$ is even max turns=$n^2-n$
if $n$ is odd max turns equals $n^2-n-1$
The minimum number of turns on an Hamiltonian path on an $n \times n$ lattice is $2n-2$ which can be constructed at least two non-isomorphic ways (rows or spiral) for each graph. The maximum number of turns Hamiltonian path onin a $2 \times n$ lattice is also $2n-2$
To maximize the number of turns, if $n$ is even then you can consider the graph to be a collection of $n \times 2$ graphs each of which can have a maximum of $2n-2$ turns in them starting from an outside corner on each side the $-2$ factor comes from the fact that in order to turn the corner you must have one vertex that does not turn, for an outside $2 \times n$ you lose one going into the corner and one from the starting/ending vertex. For the interior $2 \times n$'s you must have one "straight vertex coming in and one coming out.
$2n-2 \times (n/2)$seperate rectangles gives a formula of $n^2-n$ for even $n$.
If $n$ is odd, it is not so simple to construct a path because the rows do not divide evenly by $2$. The cases for constrcution of a maximal turning path are different if $n$ is 1 or 3 mod $4$.
If $n=1$ mod $4$ you begin again at a corner in the first row you again have $2n-2$ turning vertices in the first $2\times n$ rectangle. You then continue down the side of the graph (a $2\times (n-2)$ rectangle) and collect  $2n-4-1$ more turning vertices. Repeat on the bottom of the graph. Continue towards the starting corner now you have a $2 \times (n-4)$ rectangle that yields $2n-8-1$ turning vertices. Continue on towards the center every two new directions you turn the rectangle get smaller and there are $4$ fewer vertices. When you reach the center (where the path ends) you gain only 1 turn for the final $3$ vertices.
Putting it all together there are $n-2$ turns in the first rectangle, $1$ turn for the center and the spiral which contains $n-7+4$ rectangles in sets of two beginning with $2n-5$ turns and adding $4$ less for every set. $2n-2+1+[(n-3)(\frac{2n+5-5}{2})]=n^2-n-1$
If $n=3$ mod $4$ then you can proceed as above but the actual center vertex of the graph is contained in the last rectangle before the end of the paththe last $3$ vertices and their $1$ turn remains the same but the path is off-centered in the graph. The formula for the vertices remains the same $2n-2$ for the first rectangle $n-5$ rectangles at an average of $n$ turns per spiral rectangle and one for the last turn of the path still sums to $n^2-n-1$ for all odd $n$.
Answer to question asked in comments.
For Hamiltonian Cycles
If $n$ is odd there is no hamiltonian cycle on a $n \times n$ grid. This can be proved from the contrapositive of theorem 3.16 on page 214 of "Graphs and Digraphs" by Chartrand. By numbering the vertices of an odd $n \times n$ grid from left to right top to bottom from $1,2,3...n^2$ Select the set of vertices $S$ as all the even numbered vertices. Then $|S|=\frac{n^2-1}{2}$ and there are $\frac{n^2+1}{2}$ disconnected components so the graph cannot be hamiltonian.
If $n$ is even you can construct a "spiral" cycle like the spirals for the odd paths given above. I haven't found a closed form expression yet that deals with the center of the cycle. $(\frac{3n^2}{4}+\frac{3n}{2}-12)+C$ where $C$ is the number of turns at the center of the graph is a good description of the maximum number of turns in a hamiltonian cycle on a $n \times n$ grid.
Comment: Thanks for the response. I'm not sure I completely follow your $n$ odd case, but it seems similar to what I did.
Comment: @Michael it is necessary to demonstrate that you have obtained the maximum number of turns for each segment of vertices in the graph. The case for $n$ odd is just a demonstration that by taking smaller and smaller connected $ 2\times n-4x$ rectangles, each rectangle having all vertices turn except the one that leads to the next rectangle you have achieved the maximum number of turns.
Comment: @Robert Please contact me at my firstname.lastname@example.com Please also see my [comment here.](http://math.stackexchange.com/questions/192466/prove-b-m-c-m/192472#comment443527_192472)


Is there a way to truncate table that has foreign a key?

Question: Is there a way to truncate table that has foreign keys ? Delete and reseed can take too long. Is deleting and recreating keys only way ? If so is there a tool that does this ?
Answer: No, you either need to delete and re-create the keys, or wait for the delete and re-seed. Disabling the foreign key temporarily might make the delete faster, but it still won't allow a truncate.
ALTER TABLE [dbo].[tablename] NOCHECK CONSTRAINT ALL;

-- delete, reseed, etc.

ALTER TABLE [dbo].[tablename] WITH CHECK CHECK CONSTRAINT ALL;

Very easy to automate this by building dynamic SQL from the metadata tables, depending on exactly which table(s) you need to target. The above is just a sample to demonstrate how it is done for a single table. For example, this will do so for each table that is the target of a foreign key and has an IDENTITY column:
DECLARE @sql NVARCHAR(MAX);

SET @sql = N'SET NOCOUNT ON;';

;WITH s(t) AS
 (
   SELECT
     QUOTENAME(OBJECT_SCHEMA_NAME(referenced_object_id))
     + '.' + QUOTENAME(OBJECT_NAME(referenced_object_id))
  FROM sys.foreign_keys AS k
  WHERE EXISTS
  (
    SELECT 1 FROM sys.identity_columns
    WHERE [object_id] = k.referenced_object_id
  )
  GROUP BY referenced_object_id
)
SELECT @sql = @sql + N'
  ALTER TABLE ' + t + ' NOCHECK CONSTRAINT ALL;
  DELETE ' + t + ';
  DBCC CHECKIDENT(''' + t + ''', RESEED, 0) WITH NO_INFOMSGS;
  ALTER TABLE ' + t + 'WITH CHECK CHECK CONSTRAINT ALL;'
FROM s;

PRINT @sql;
-- EXEC sp_executesql @sql;

It may be that the output gets truncated, but this is just a limitation of PRINT (8K) - the actual command is complete.
PS this assumes SQL Server 2005 or better. Always useful to specify your version as part of your question (usually with a tag).
Comment: While developing, to clear and set new test data.
Comment: @IvanP: Assuming this is part of an automated process, it's fairly simple to identify which tables have FKs.  `DROP` those first, then recreate your schema in reverse order.
Comment: Script must be updated for every change in table, don't need that.
Comment: I thought you were talking about static script and recreating whole table structure.
Comment: I thought [we're not supposed to do variable concatentation](https://dba.stackexchange.com/a/132709/220697)
Comment: No, I realized that you might not have known. Was just wondering whether to edit this answer which I came across recently, but wouldn't be so rude as to do it without asking. By the way, the problem can also manifest in joined queries and parallel plans.


Rheem T-Rex 13 tankless water heater 6awg 3 wire 60amp

Question: Can I run my Rheem T-Rex tankless water heater on same 60amp breaker as my 240v dryer? Can I put in a junction box at my dryer area and run power to the tankless water heater?
Comment: I'd have concerns about the performance of a tankless heater that is only 60 amps. That's barely bigger than a British electric shower. The #1 mistake people make with tankless heaters is scrimping on heater amps, or "compromising" because they can't power a large enough heater.  This usually ends in project failure and blaming tankless tech (wrongly). OTOH 60A would be ideal for point-of-use e.g. in a bathroom.  Instant shower - no pipe wait!
Comment: @Harper-ReinstateMonica And the #2 mistake is getting a really big tankless heater without considering their overall electric service capacity.
Comment: Most dryers are the 30A not 60A. You need a subpanel.
Comment: And two single 30 amp breakers handle tied does not equal 60 Amps
Comment: It would be a code violation to have a standard dryer on a 60a breaker. What are the requirements for the T-Rex as listed in the mfg instructions? A sub off that 3 wire may be possible if black white red, you can add a ground. Note the neutral is normally required for a dryer so moving wires around and adding a ground to feed a sub is possible, more info is needed.
Comment: Why do you want a tankless water heater here?
Comment: Was just noticing the HD reviews, 14% 1 star, and many of 4/5 star are for larger models.
Answer: A typical US residential clothes dryer uses a 30A 240V circuit. The wiring is almost always sized appropriately (10 AWG) and not suitable for any larger load. There seems to be a bit of a debate about whether you could use 2 30A receptacles on a single 30A circuit, but while that might allow a 30A dryer + 30A kiln or 30A dryer + 30A water heater, it won't allow a 30A dryer + 60A water heater or a 60A water heater by itself.
Looking at it in reverse, if you had a 60A circuit with appropriately sized wires, you could not put a 30A receptacle on the same circuit. So you really need to have each circuit sized correctly to the load and to the wires. Most of the time that is quite straightforward, though there are some exceptions at (15A and 20A receptacles allowed on 20A circuits, certain types of motors allowed to have larger breakers based on startup current, etc.)
So you need more power and bigger wires and a way to connect 2 or more circuits to get their portion of the power. That's a subpanel.
The recommendation right now, based on wire pricing, is to use large aluminum (e.g., 2 AWG for 90A) to feed from the main panel to the subpanel, and then install whatever you need in the subpanel. A 90A subpanel can handle a water heater + 30A dryer, and can normally have some smaller circuits in the same panel as well, even though the total based on breaker handles will be more than 90A.
Related is a load calculation. Before adding a new large load such as a 60A water heater, you need to make sure your existing main electric service is up to the task, in the utility feed, main breaker and panel specs. If your panel is rated for 200A and has a 100A main breaker, you can't just swap it for a 200A breaker without (most likely) upgrading the wires from meter to panel and checking with the utility to make sure they can supply that level of power. Similarly, even if the utility says 200A is fine, if your panel has a 150A breaker and you already have lots of other large electric loads, you may find that adding the 60A water heater will push you over the 150A, leading to main breaker trips (not fun). You can upload a picture of your panel and answer a bunch of questions here and get a reasonable recommendation, or get a qualified electrician to review everything on-site.
Answer: In order to avoid overload or high installation costs, a special device could be used, which is a sort of XOR power switch.
There are many different names for this item, f.e. shower priority switch/contactor, load shedding switch, Lastabwurfrelais/Lastabfallrelais/Lastabwurfschalter (german).
The english wikipedia page on this subject seems to be still missing, here is a translation:
https://de-m-wikipedia-org.translate.goog/wiki/Lastabwurfrelais?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en-US&_x_tr_pto=wapp
A tankless heater for showers can/should be combined with a counterflow heat exchanger, which saves money and energy and/or improves the comfort.
For DIY- exchangers, see the youtube videos of "Rob the plumber".
Local codes need to be considered, f.e. in some locations, between fresh and drain water a double wall construction is mandatory.
Answer: As @xeeka alludes to, this can be done, but needs to be done right.  You'd be well advised to get a professional electrician and a permit.  Set it up like so
<code>  main panel ---60A breaker---switch------------------- Tankless
                                  \-------30A breaker-- Dryer
</code>
Your single 60A breaker needs to feed a switch.  At any one time all the power must to either the tankless or the 30A breaker for dryer, never both.  The switch must be rated for hot disconnect, in case a full 60A is being pulled by the tankless unit at the time the switch is actuated.
Let me be clear: this is a DIY activity only at a high level. You're well advised to get a professional to make this setup.

A device I sometimes install is a tank booster.  That device boosts the outgoing temperature of a tank heater to 120F.  It runs off the same 30A breaker as the electric water heater, but it's greedy.  When it's running it temporarily turns off power to the tank water heater.
This device is used when the main tank is too small for the need, deliberately kept at a low standby temperature for energy savings, or when recovery is slow as in with solar or heat pump systems.  That lukewarm water is boosted to full strength instantly.
Comment: @FreeMan take a look at the diagram.  The 30A dryer is on a 30A breaker, as diagramed above.


Hardness of Approximation of MAX-3SAT

Question: This is probably a duplicate of this question, but I need a somewhat blunter answer.  Let's say I have a polynomial time algorithm that finds an assignment that satisfies more than $\frac{7}{8}$ of the clauses of a satisfiable 3SAT instance.  Do I collect my million dollars from the Clay Institute for proving $P=NP$?
Answer: I believe that Håstad gave such an algorithm in 2000, see On bounded occurrence constraint satisfaction. His algorithm is stated for instances where each variable occurs at most $B$ times, and the advantage over 7/8 depends on $B$. The running time, however, seems not to depend on $B$.
In order to prove that P=NP, you need to find an algorithm which, given a satisfiable instance, satisfies at least $7/8+\epsilon$ clauses, for some constant $\epsilon>0$. This will enable you to distinguish between satisfiable instances and instances which are at most $7/8+\epsilon/2$ satisfiable, which is NP-hard as my answer to the question you mention shows.
Comment: Aha, I think I get it.  To keep it concrete, distinguishing between 7/8th satisfiable and 100% satisfiable is in P, distinguishing between 89% satisfiable and 100% satisfiable is NP-hard (where that 89% is constant and independent of the problem).  You could use my hypothetical 90% solver to solve the real satisfiability problem by reducing an input formula $\phi$ in polynomial time to another formula $\phi'$ such that  $\phi'$ is 90% satisfied iff $\phi$ is SAT.  But if you can only achieve 7/8th, then you have gained nothing.
Comment: I _think_ I understand the difference, but now I'm further mystified.  Let's say my hypothetical algorithm finds an assignment that satisfies 90% of the clauses for a satisfiable instance.  Now it is presented with a problem where the maximum proportion of satisfiable clauses is, like, 95%.  How would my 90% algorithm distinguish between the two?
Comment: Your algorithm doesn't distinguish between these two cases. It distinguishes (for example) between satisfiable instances and those that are at most 89% satisfiable.
Comment: Right, you got it. It is actually conceivable that 89% or 90% could be improved to $7/8+f(n)$ for some $f(n)=o(1)$, but I'm not aware of any such result in the literature, and I don't know whether current technology is good enough to prove such a bound.

Hardness of Approximation of MAX-3SAT


Wordcount subfiles

Question: Im having a problem with the wordcounter in overleaf v2 not counting the words in the subfiles, but only in the main tex, is it somehow possible to make the word count include subfiles?
Comment: If you are open to alternatives, there is my answer here, https://tex.stackexchange.com/questions/596489/counting-words-and-characters-with-or-without-whitespace-with-texcount/596965#596965, which can examine external files.
Answer: I'm not familiar with Overleaf, but as I understand it uses TeXcount to do the word count.
TeXcount has multiple options, including options for including subfiles: eg the -merge option. However, this must be provided to the TeXcount command line, which Overleaf apparently does not.
The Overleaf page on word counts has a section on How to run texcount with custom parameters, but the solution this provides is to use \write18 to execute TeXcount from within LaTeX, and then include the resulting output into the document. This is a pure TeX/LaTeX solution which executes TeXcount when you typeset the document, not from the word count menu.
Given that this is Overleaf's suggestion, I assume they don't have a solution that modifies the behaviour of the word count menu item. Perhaps it could be suggested to them to add it.
An alternative would have been if TeXcount was able to turn on subfile inclusion from within the TeX code, but it doesn't.
Related question:
Total word count using texcount

Wordcount subfiles


Fetch unique values using visual workflow

Question: I am creating a dependent picklist in visual workflow using dynamic choice elements. The data source for picklists is database. When I fetch values I am getting duplicate values as it is in the database. Any way to fetch only the unique values.
Comment: It might be worth taking a look at the new SObject Collection and Loop features coming in Summer'14 for this.
Answer: Can you create a custom object for maintaining these picklist values and dependencies?  Then you can reference the custom object in your dynamic choices and get unique values.


Does image on the page improves SEO rankings?

Question: My friend once told that I should include big image on the main page of my website. And it will be good for SEO.
So does image on the page improves SEO rankings?
Answer: Yes and no.
It is content that ranks and image tags offer some to the total performance of the page, however, it is limited.
Where your friend is right is engagement. Google looks for elements that offer engagement. An image is the most basic engagement there is. At one point, Google was not shy about saying that an image should exist at the top of the content. SEO's agreed for several reasons and so for almost every page you will see on the web, there is an image at the top of the content.
So besides the value of the alt text and any potential that the path and file name give, Google credits the image as engagement. However, this too is limited.
From a user experience (UX) perspective, it does cause a pause in the users visit and may entice the user to read your content. It is just one element, however, it is the UX effect that is the greatest. It can extend the time spent on page and reduce bounce rates somewhat which are other metrics Google can use to rank a page.
Answer: Google robot  is  text  crawler - so  it can't "see" image (ony the code of image).
But big image could slow down you page - and  that can give you some negative ratings  (you can measure it  here https://developers.google.com/speed/pagespeed/insights/)
On the other  hand there is  User Experience ( you are creating website for people, not for robot) , and IMHO it's more important to have a good looking site(even with a ton of graphics) with a good  content  than  plain text site with better  seo rating :D .
Answer: Good picture may look attractive for users, and yes, it can extend the time spent on page, but make sure that it does not affect on page's speed - it irritates visitors.
Answer: Yes, Image on the page do increase the SEO rankings. When image is added with certain determination, it will help to understand the article clearly. Use images to every article you write online. It will attract the readers because the first view is not just a text.


How can I enable the drivers for beats audio speakers for hp envy dv6?

Question: I recently shifted to Ubuntu.
My beats audio speakers connected to my laptop are not working.
I am using an hp ENVY dv6 laptop.
What should I do?
Comment: Try with installing sound driver packages `sudo apt-get install linux-sound-base alsa-firmware-loaders alsa-oss alsa-source alsa-tools alsa-tools-gui alsa-utils alsamixergui alsaplayer-alsa alsaplayer-common alsaplayer-daemon alsaplayer-esd alsaplayer-gtk alsaplayer-jack alsaplayer-nas alsaplayer-oss alsaplayer-text alsaplayer-xosd libsox-fmt-alsa alsa-base`. Reinstall the present ones.
Comment: ^ this does not work
Answer: This was done in my own HP envy and this process works on all HP laptops containing beats audio.
STEP 1
Install hda-jack-retask from https://launchpad.net/~diwic/+archive/hda . Download this small application according to your version of Ubuntu. After the completion of download, install the app.
STEP 2
After the app is installed, go to the terminal and type hda-jack-retask which opens the file. Open app using terminal
STEP 3
At the top, in codec section, select IDT 92HD91BXX codec.
This code varies with various models. Check it STEP 4
Check the " Show unconnected pins" at the right side. STEP 5
After this, you will see different types of unconnected pins of your sound driver. You have to map these pins to the right part of the beats audio drive. Care must be taken at this point.
You can see there are various types of pins. We are not aware about these things. Even I don't know
what I am doing and is confusing. BUT do not worry at all.
You just have to play on three pins. They are 0x0d , 0x0f and 0×10.
STEP 6
Go to the section having pin id : 0x0d .
Change (Internal Speaker, Front side) to "Internal speaker".
STEP 7
Go to the section having pin id: 0x0f.
Change (Not connected) to "Internal speaker". This part is about the under-display speakers.
STEP 8
Go to the section having pin id: 0×10.
Change (Not connected) to "Internal speaker (LFE)". This part is about the sub-woofer.
STEP 9
You are finally done with those pin settings. Apply it now. You can test with some sound. Check whether all the speakers are producing desired sound. The settings must be done as in following picture.
Do as it is
STEP 10
If everything is all right, install boot override from the bottom right side and restart your device.
Finally you must have sound with beats audio. Enjoy the sound and music. Also plug in the headphones, it must disable the external sound when the headphone is plugged in.
you can visit here for more information. http://www.chromeearth.com/enable-beats-audio-in-ubuntu/
Comment: this no longer works on 18.10 - when i click apply now it tells me `device or resource busy`
Comment: In Ubuntu 18.10 you can't use "Apply Now" option to test, but directly set "Install Boot Override" and test it in the next reboot.
Comment: is there any way to write terminal scrip for this?
Answer: Please note that Steps 1 and 2 above no longer work as written.
Rodrigo Tessarollo's fix worked but he did not detail what changed. David Henningsson's PPA 'HD audio related stuff' at https://launchpad.net/~diwic/+archive/ubuntu/hda has not been updated since 14.04. His alsa-tools-gui which includes hda-jack-retask is now in the Ubuntu repositories.
Step1 is now install alsa-tools-gui via terminal with sudo apt-get install alsa-tools-gui or with Synaptic or some other Package Manager.  It does not show up in the new 16.04 Ubuntu Software Center.
Step 2 is to enter "HDAJackRetask" into the Unity Dash to open the app.  Note the way it is written.
Then follow step 3 on as stated above by @Bipin Paudel.
Comment: This worked for me on the latest Pop!_OS 19.10 on my HP Envy 17" TouchSmart, now have fairly decently working speakers on Linux.
Answer: I had the same issue with my HP Pavilion DV6, and solution is probably the same:
Open the terminal, type sudo gedit /etc/modprobe.d/alsa-base.conf and add the next line:
options snd-hda-intel model=ref

where ref is Your laptop model, typed in the same order as your default hostname during installation of ubuntu.
Mine for example was:
options snd-hda-intel model=HP-Pavilion-DV6-7031tx

Then, restart the device and see if it works. If not, here is useful solution on how to do that, but I do not know if it will work on Your model.
Beats audio driver for hp dv6-7040tx
Answer: The only solution that I have found so far is to retask the audio using "HDAJackRetask" which is part of the "alsa-tools-gui" package.
This worked for me on my Pavilion DV6 7014NR running ubuntu 15.04 x64.
You can follow this tutorial, simple and fast & graphical way: http://www.smittix.co.uk/beats-audio-subwoofer-not-working-correctly-ubuntu-14-04/


How to force display of a specific page of paged data

Question: I'm displaying a table of dated items ordered from old to new and am using the full pager. How can I force my page to initially display those items that are current ie. on initial load, display the page containing items that are most current (which might be ?page=17). The user can then page back/forwards to get older or newer items. Drupal 8.
Answer: I'm half way there!
In hook_views_pre_build(\Drupal\views\ViewExecutable $view) I figured that the $cnt item was the most current; from there it was a simple matter to calculate which page that item would appear on and to set that as the current page.
<code>$pager = $view->getPager();
$defaultPageNum = round($cnt/$pager->getItemsPerPage());
$pager->setCurrentPage($defaultPageNum);
</code>
This works like a charm; however, the pager links at the bottom of the page do not auto-magically update and still indicate that I'm on page 1 (instead of page 62).
Anyone know how I get these links to update?


Web Payment API/Services that can be easily integrated with Rails

Question: What are some of the popular web payment API/services that can be easily integrated with ruby on rails framework? I have tried using PayPal the standard version and it was not too flexibler. I have never tried the pro version. Can you guys suggest other alternatives out there that are easy to use, secure, not too hefty on the commission as well and have subscription/recurring payment functionality.
Answer: There is Stripe. You can see nice short screencast by Ryan Bates here: http://railscasts.com/episodes/288-billing-with-stripe
There are also two other options with screent cast, namely PayPal http://railscasts.com/episodes/141-paypal-basics
and Active Merchant http://railscasts.com/episodes/144-active-merchant-basics
Answer: Authorize.net has an API with sample code for Ruby and several other languages.  No direct rails plugin, but I am sure it can be easily incorporated.  I used the PHP version and incorporated it in under an hour.  It has all the functions that you mentioned in your post.


What was the Japanese or Axis motivation to drag US into the War?

Question: Making an enemy out of a neutral country when you are at war with many others means there is one more enemy to fight. So what was the plan of Japan or the Axis to drag US into the war? Did they think they could make the US a Japanese colony? If so how did they plan to win such invasion?
Comment: Who were these "many" enemies that Japan was fighting?  Japan was in a war with China, before December 1941.  Who else?
Comment: Your question will be much improved if you can quote one example such as Pearl Harbor attack by Japan with your own research and understanding. Your question sounds like they wanted to drag the US into the war and is there any reference?
Comment: I don't think the Germans tried to drag the US into the war -  quite the opposite, in fact.  There was IIRC still quite a bit of pro-German sympathy prior to Pearl Harbor.  (Recall that the Holocaust wasn't really known, or at least believed, until much later.)  The Japanese intended to take at least the Pacific, including US posessions such as the Phillipines, so wanted to knock out the US fleet, thinking that would cause the US to retreat to the mainland.
Comment: Hitler certainly did plan to create a colony out of the United States—in fact, he had detailed plans for how to defeat the US. (see [this](http://history.stackexchange.com/questions/15554/how-did-the-nazis-plan-to-defeat-america-during-world-war-ii)) Evidence for this is that he started training the 8-member spy ring which was to sabotage American factories—BEFORE the US entered the war.
Answer: Neither Japan nor Germany intended to actually invade the United States. Instead, they saw the US as a threat to their plans for conquest of SE Asia and Europe.
Japan
Japan and the US saw each other as rivals for control of the Pacific. They had the largest fleets, and overlapping interests. The US had its island territories won in the Spanish-American War, primarily the Philippines, it would protect. Japan, increasingly isolated by the international community for its violations of treaties and war in China, was looking to secure natural resources. Tensions were high.
With its vital imports cut off by embargo, Japan planned an invasion of the Dutch East Indies (DEI) for oil, rubber, and other natural resources. However, look at this map.

Red = Japan
Blue = US
Yellow = Britain
Purple = France
Orange = Dutch

If Japan attacked DEI, Britain, France, and the US all have major colonies with military bases positioned between Japan and DEI. They all favored the Dutch, and they were all wary of Japan.
Once France was defeated in 1940 they were no longer able to defend their Pacific colonies. Japan took defacto control of into French Indochina effectively knocking them out of the coming Pacific war.
Britain and the US, on the other hand, possessed powerful Pacific fleets capable of cutting off Japan from DEI. They could attack vulnerable transports carrying precious oil and resources back to Japan. Japan decided they would have to deal with these fleets, and their bases (Pearl Harbor, Singapore, Manila, Hong Kong), if they were to take and make use of the resources of DEI.
They decided on a pre-emptive strike to destroy the US Pacific fleet at Pearl Harbor while invading all US and Allied possessions to deprive them of bases. The hope was not to defeat the US completely, but to demoralize her and destroy her ability to project power. By the time the US fleet had been rebuilt, Japan would have a fortified ring of defenses and could negotiate a peace.
That was the idea anyway. The US surprised everyone not only by staying in the fight, but by building several new fleets in the middle of a war.
Germany
Germany's motives remain unclear. Germany had long been annoyed by the US's increasingly open support for Britain including arms, food, and ships. US destroyers sparred with German submarines even while neutral. However, while the US government was mobilizing and becoming ever more allied with Britain, US popular sentiment was against war with Germany.
Shortly after Pearl Harbor, Germany declared war on the US. This was done by Adolf Hitler without consulting his advisors. Numerous theories abound as to why, the strongest is he hoped Japan would in turn declare war against the Soviet Union. However, both the Anti-Comintern Pact nor the Tripartite Pact between Germany and Japan were both defensive; they did not compel Japan to join an offensive war.
Japan felt betrayed that Germany signed the Molotov-Ribbentrop Pact with the Soviets in violation of the Anti-Comintern Pact right as Japan was fighting the Soviets at Khalkhin Gol, a fight that did not go well. As a result, Japan ended their ambitions towards the USSR and looked south instead. By December 1941, Japan had just started a war with China, the US, and Britain. They had no interest in opening another front with the Soviets.
Declaring war against the US was probably Hitler's biggest blunder. Faced with the threat of Japan, the US likely would have thrown it's might into that fight and ignored the European problems. Instead, Germany was now at war with an enemy it had little ability to strike at, though there was about nine months of slaughter as German U-Boats ran rampant over the ill-prepared US coastline.
US industry, manpower, and warships could now freely support the Allies. Despite having been attacked by Japan, the US focused on Germany.

Germany and Japan had some ideas about how to strike at the US. Few were practical, even fewer were actually built, even fewer would have affected the war.
The Japanese had the I-400 class submarine. Each carried three small aircraft. The Japanese planned to build 18 and use them to strike the Panama Canal and prevent the US from moving ships to the Pacific. This might have had a strategic effect on the war had they been used early enough. Instead, they built 3 so late in the war they were never used for their intended purpose.
Germany had the Amerika Bomber, a long range bomber intended to attack New York City. It was overambitious and as the war progressed Germany lacked the resources to develop such an aircraft. The program was scrapped.
Comment: Declaring war on the US allowed Germany to actually *attack* (ill-defended) US shipping, in the hopes of strangling Britain. Germany's time was rapidly running out; the war was turning from one of tactical movement (favoring Germany) to one of attrition (favoring the USSR). Once that happened, Germany could only prolong the war, not win it.
Comment: As far as Hitler was concerned "it was time" whatever that means. Certainly the 3rd Reich didn't see much negative impact from an American entrance in World War 2 on the sides of Soviet Russia and Great Britain. This turned out to be a huge blunder actually. As far as Japan's motivation many Historians believe Japan was provoked into War by the resource embargo under FDR. This of course would preclude the use of Japanese controlled Manchuria at the time as a place for said resource exploitation which of course would be false. I would argue Japan was being greedy by attacking USA Dec 7th, 1941
Answer: No Japan never planned to make USA a colony, or to invade the continental territory of the US. The main immediate reason of the war was the economic embargo imposed on Japan by the US (and the reason for the embargo was Japanese invasion of China).
Answer: Hitler's Fatal Miscalculation, by Klaus H Schmider (Cambridge University Press, 2019) is a detailed examination of the information Hitler had at the point he declared war on the USA on 11th December 1941. The conclusion is that it looked like a reasonable idea at the time:

The attack on Moscow had bogged down, but the German command structure and most of the commanders on the Eastern Front reckoned they'd damaged the USSR so badly that it would only be capable of defensive warfare thereafter. That started to look dubious the next day, and was disproven by the end of January.

The Japanese had committed themselves to war, and offered alliance. Given the tortuous negotiations between Germany and Japan over the previous three years, as the various Japanese factions tried to form a consensus for very different policies and objectives, the offer of an alliance might well vanish if it was not accepted.

Hitler regarded the repeal of most of the remaining provisions of the American Neutrality Act of 1939 as a signal that war with the US was months away, at most. Declaring war himself put him in a position of control, and thus looked better politically, by Nazi standards.

Hitler knew by mid-January 1942 that he'd made an error, but had no way to back down without looking weak.
Answer: The Axis countries attacked the United States as a "deterrent." Take Japan at Pearl Harbor. The intent was to "knock out" the U.S. fleet for two years, during which Japan planned to conquer Southeast Asia (which she did) plus China and India (she came fairly close). The expectation was that by January 1, 1944, Japan would be confronting the U.S. with a behemoth consisting of Japan, China, India, and today's "ASEAN" nations, and the U.S. Would have no choice but to make peace.
What Japan didn't count on was American resilience. Six months after Pearl Harbor, a "weaker" American fleet knocked out four Japanese carriers (about half of Japan's striking power at Midway, while suffering only one quarter of the losses (a single carrier). Combine this with Japanese losses at Coral Sea and Guadalcanal, and the Japanese fleet was basically "done for" (it had one last hurrah in waters around the Philippines in mid to late 1944). By mid-1944, the Americans had "island hopped" the central Pacific from "Tarawa to Tinian," the latter on Japan's doorstep, effectively separating the Japanese islands from her Asian possessions.
Then Germany's Admiral Doenitz felt that he could knock out America's merchant marine by sinking ships faster than they could be built. He was correct for 1942 that he could sink faster than we built, but the Americans still managed to land a large enough force in North Africa in November, 1942 to draw away enough German supplies and reinforcements from the battle of Stalingrad so that the Russians could win, followed by an invasion of Italy in 1943. (The Axis had not expected America to make its weight felt until 1944, by which time Germany expected to have conquered Russia, and possibly Britain as well.)
The Axis tried to "buy time" with pre-emptive strikes on America, but given the speed and severity of the American reactions, and the holding out of America's other allies, they didn't buy enough time.
Answer: Ian Kershaw's biography of Hitler has some interesting insights (pp656-660 of the single-volume edition).
Hitler felt that the Japanese would tie down the US in the Pacific, and weaken the British by attacking their Far East possessions. He was also delighted to have "an ally which has never been conquered in 3000 years." He had given the Japanese a verbal commitment on 4th December 1941 that if war broke out between Japan and the USA, Germany would consider itself at war with the US too, and Italy had willingly joined this new tripartite pact. That was completed on 11th December as a commitment by all parties not to make a separate peace with the USA.
Hitler felt that FDR was looking for an excuse to intervene in Europe, and the general German opinion was that if the US was at war, there would be no more Lend-lease for the British: the US would want all its war production for its own use.
He formally declared war on the US in a speech to the Reichstag later on 11th December. He felt that this formalised what was already the effective situation, and demonstrated that he was still in control of events. Waiting for a declaration of war from the USA would have been a sign of weakness, in this thinking. His primary target for this speech was the morale of the German population; this was a way to get them to view a new opponent as a positive development.
He underestimated all his opponents, the US most of all.


How do I restore the Grub menu?

Question: I lost my password and booted into the command line from the Grub menu. Now my PC does not want to boot into Ubuntu. Every time I reboot, I end up at the Grub command line. Is there any way to restore the Grub menu? I can boot into Ubuntu using Grub command line commands.
Answer: Since you lost your password, it sounds like you just need to change your password to get a normal boot.  To do this hold down your shift key during boot up.  Select recovery mode (which is usually the second entry).  Wait for boot up process to complete.  There will be a list of options.  The one that you want is the Drop to root shell option so press the down arrow to get to that option and press enter to select it.
The root account is the ultimate administrator and can do anything to the Ubuntu installation (including erase it) so be careful with what commands that you enter in the root terminal.  If the file system is mounted as read only, you will need to enter:
mount -o rw, remount/
in the terminal
Now to reset the password, type:
passwd username
where username is the user name you want to reset.  Substitute your username.  You will then be prompted for a new password.  When you type the password you will get no visual response acknowledging your typing.  Hit enter when you are done.  You will be prompted to retype the password.  Do so and hit enter again.  Now the password should be reset.  Type:
exit
to leave the terminal.
Comment: What does the GRUB prompt look like?  There is a GRUB rescue tutorial at https://linoxide.com/grub-rescue-commands/.  It may be of assistance.
Comment: I cannot get to the recovery mode screen, my PC boots straight into the Grub command line. Pressing left shift, right shift or ESC do not work.

How do I restore the Grub menu?


How to get a good staff

Question: I want to be able to find a strong staff to help me? Thanks and please share your ideas. I have tried searching dungeons and things but I have not found one strong enough. About 50-60 damage.
Comment: You are going to need to give us exactly what you mean by 'Good' or 'Strong Enough' for us to be able to answer your question.
Comment: 50-60 damage.....
Comment: Edit your question to put that and any other information in it :) Click the Edit button and have at it.. Tons of us have hundreds of hours in Skyrim, we can help you find something!
Answer: Staves that can deal 50+ damage are often rare and require a high-leveled character before they will appear as loot in chests or in the inventories of shops that would sell them (typically mage shops and general stores).
That said, there are a few staves that are not randomly generated, and they are typically held by Dragon Priests. There is a Staff of Icy Spear towards the end of the Dawnguard expanion's quests (In the Inner Sanctum) on a frozen Falmer.
If you have the Dragonborn expansion, it is possible after a certain point to enchant your own staves. To do this you'd need the required materials, and have learned the spell (Icy Spear, Incinerate, Wall of [element]) that you wish the staff to be.
Answer: Ok first of all those staves are extremely rare and take a while to get, but you could always do the college of winterhold quests to get the staff of Magnus which is pretty good but you have to beat a dragon priest so for these staves you have to be a high level especially if you're playing on master or legendary.

How to get a good staff


Ideal classes fixed by the Galois group

Question: Let $K$ be a number field and let $G$ be the group of automorphisms of $K$ over $\mathbf Q$. The group $G$ acts in a natural way on the ideal class group of $K$. I would like to know if there are any results giving a formula for the number of orbits of this action (or equivalently a formula for the number of ideal classes that are fixed by some element of $G$). In particular, I would like to compare the number of orbits to the class number of $K$.
Comment: look up ambiguous class number formula and genus theory.
Comment: @MatthiasWendt: the Galois group of a quadratic field $K$ can act trivially on the ideal class group of $K$ even if the class group is nontrivial. For example, let $K = {\mathbf Q}(\sqrt{-5})$, with class group of order 2 generated by the ideal class of the prime $\mathfrak p = (2,1+\sqrt{-5})$. This prime ideal is fixed by the Galois group, so its ideal class is fixed. Therefore the Galois action on the ideal class group is trivial. More generally, if all elements of the class group have order 1 or 2 then the Galois action on ideal classes is trivial since ideal classes of primes are fixed.
Comment: There is some literature about Galois module structure of K-groups. I think what you are asking can be reformulated in terms of the Galois module structure of $K_0$, so that literature might contain the answer to your question. Unfortunately, I am not a suitable guide through that literature.
Comment: @KConrad: you're right, of course. I removed my comment.
Comment: Is there an elliptic curve analogue of the ambiguous class number formula in literature, i.e. an analogous result for say the Selmer group or p-part of Selmer groups?
Answer: I assume you want $K$ to be Galois over $\mathbb{Q}$. More generally, let $L/K$ be a Galois extension of number fields. The the class group $C_K$ of $K$ maps to $C_L^{G_{L/K}}$, the part of $C_L$ fixed by the Galois group of $L/K$, and you seem to be asking what the quotient $C_L^{G_{L/K}}/C_K$ looks like.
Taking cohomology of the exact sequences
$$ 1\to R_L^*\to L^*\to L^*/R_L*\to1
\quad\text{and}\quad
  1\to L^*/R_L* \to I_L \to C_L \to 1
$$
gives (if I'm not mistaken) exact sequences
$$
  0 \to H^1(G_{L/K},L^*/R_L*) \to H^2(G_{L/K},R_L^*) \to \text{Br}(L/K)
$$
and
$$
  0 \to C_K \to C_L^{G_{L/K}} \to H^1(G_{L/K},L^*/R_L*),
$$
so the quotient that you're interested in naturally injects
$$
  C_L^{G_{L/K}}/C_K \hookrightarrow
  \text{Ker}\Bigl(H^2(G_{L/K},R_L^*) \to \text{Br}(L/K)\Bigr).
$$
The Galois structure of unit groups has been much studied. You might look at some of Ted Chinburg's papers (http://www.math.upenn.edu/~ted/CVPubs9-10-07.html)
Answer: As Franz Lemmermeyer suggested, one should consider the so-called Ambigous Class Number Formula: you find it, for instance, in Gras' book "Class Field Theory", II.6.2.3.
It says that if $L/K$ is a finite cyclic Galois extension with group $G$ and if we denote by $Cl_L,E_L$ the class group and the unit group of $L$ respectively (and likewise for $K$), then
$$
\vert Cl_L^G\vert=\frac{\vert Cl_K\vert\cdot Ram(L/K)}{[L:K]\cdot [E_K:E_K\cap\mathrm{Norm}_{L/K}(L^\times)]}
$$
where $Ram(L/K)$ is the product of all ramification indexes of finite and infinite primes of $K$ in the extension $L/K$.
So, in case $K=\mathbb{Q}$, you get simply
$$
\vert Cl_L^G\vert=\frac{Ram(L/\mathbb{Q})}{[L:\mathbb{Q}]}\quad\text{or}\quad \vert Cl_L^G\vert=\frac{Ram(L/\mathbb{Q})}{2[L:\mathbb{Q}]}
$$
according as whether $L^\times$ contains or not an element of norm $-1$.
The proof is basically cohomological following the one suggested by Joe Silverman: the term $Ram(L/K)$ comes from fixed ideals in $I_L^G$ and the index of the norm of units of $L$ inside those of $K$ controls some capitulation kernel - but you can look in Gras' book for details.
In case of dihedral extensions, you can look at the question Class groups in dihedral extensions - some sort of Spiegelungssatz?
Comment: For $\mathbb{Q}(i)/\mathbb{Q}$ this gives $1/2$. Is there perhaps a missing factor of $2^{r_2}$?
Comment: Thanks, my formula was wrong! I should consider finite and infinite primes, so that $Ram(\mathbb{Q}(i)/\mathbb{Q})=4$.
Comment: You should assume that $L/K$ is cyclic. Consider $\mathbb{Q}(\sqrt{-3},\sqrt{13})/\mathbb{Q}$. Also replacing $13$ with any prime $p$ satisfies $p\equiv 1 \bmod 12$ is a class of  counter-examples.
Comment: @J.Li Oh, thanks, sure! Corrected.
Answer: Since the map $j$ from $C_K$ to $C_L^{\operatorname{Gal}(L/K)}$ is not always injective, we are looking at the cokernel of this map. $\operatorname{coker} j$ will map onto $$H^1(\operatorname{Gal}(L/K),L^\times/R_{L^\times})= \ker\left(H^2(\operatorname{Gal}(L/K),R_{L^\times}) \to \operatorname{Br}(L/K)\right)$$ with kernel equal to the natural image of $H^1(\operatorname{Gal}(L/K),U_L)$ in $\operatorname{coker} j$, $U_L$ the idele units. In particular we have an isomorphism when $L/K$ is unramified.
The ambiguous class number formula applies only to cyclic extensions $L/K$.

Ideal classes fixed by the Galois group


How can one display local time and date to my drupal website visitors depending upon their geographic location?

Question: I need to display the FIFA world Cup 2010 schedule on my Drupal website. But what I want is that each visitor should be able to see the time for the upcoming matching as per his/her own geographic location . How can this be done ?Any suggestions would be welcomed. Thanks for reading this through.
Answer: You need to be able to sniff the user's location. The most common way of doing that is by using an IP-to-location service or library. There are freely available IP-to-location libraries which provide country-level resolution, or you can pay to get data that is accurate down to city level.
There is a contrib module which allows you to incorporate the MaxMind GeoIP more easily. http://drupal.org/project/geoip
Answer: I think what you need is a tool like GeoIP,  i don't know Drupal so this is just a hint... just a thought!
Answer: You can put a time zone spinner with the World Cup schedule on your website, and let your users convert the match times to their local time if they select their local time zone from the spinner.
Answer: What about JS getTime()?  Wouldn't that work in browser and pull from the user's settings on locale?


If $H$ is a Hilbert space and $M$ is a closed subspace of $H$, then $H/M$ is a Hilbert space

Question: Can anyone give a brief proof or a reference of a proof for the following property of Hilbert spaces?

If $H$ is a Hilbert space and $M$ is a closed subspace of $H$ then $H/M$ is a Hilbert space.

Definitions:

A Hilbert space $H$ is a real or complex inner product space that is also a complete metric space with respect to the distance function induced by the inner product.
A closed subspace of $H$ is a linear subspace of $H$ that is closed with respect to the topology induced by the norm (which is induced by the inner product).

I know that $H/M$ denotes the quotient set. But I don't know how to prove the Hilbert space structure on this set.
Answer: First of all, note that $H/M$ is a normed linear space, with the norm $$\|[x]\|_{H/M}=\inf_{y\in M}\|x-y\|_H,$$
where $\|\cdot\|_H$ is the norm induced by the scalar product on $H$. To show that $H/M$ is a Hilbert space, we need to show two things: that $H/M$ is a complete metric space (under the metric induced by $\|\cdot\|_{H/M}$) and that $\|\cdot\|_{H/M}$ is induced by an inner product.
We can do this by the following three steps:

Show that $H/M$ is isometrically isomorphic to $M^\perp$ via the map $\psi\colon H/M\to M^\perp$ defined by $\psi\colon [x]\mapsto P^\perp x$, where $P^\perp$ denotes the orthogonal projection of $H$ onto $M^\perp$.
Note that $M^\perp$ is a closed subspace of $H$. Since $H$ is a complete metric space, and closed subsets of complete metric spaces are complete themselves, this shows that  $M^\perp$ is a complete metric space. Show that this, together with the isometry, means that $H/M$ is complete.
Recall that a norm on a linear space is induced by an inner product if and only if the norm is subject to the parallelogram law. Note that since $\|\cdot\|_H$ is induced by an inner product, it must satisfy the parallelogram law. Use the isometry to conclude that $\|\cdot\|_{H/M}$ also satisfies the parallelogram law, and thus is induced by an inner product, just like we wanted to show.
Answer: I will show you that if $X$ is Banach and Y is a closed subspace then $X/Y$ is Banach. From this hopefully you can extrapolate to your case. Now, you just need to define an inner product on your factor space.
To that end, let $X$ be Banach and $Y$ a closed subspace, and let $\{X_n\} \subset X/Y$ be an absolutely convergent series in $X/Y$, i.e, $\sum_{n \in \mathbb{N}}{\|X_n\|_{X/Y}} < \infty$. Recall that our quotient norm is defined as
$$\|x\|_{X/Y}=\inf_{u \in x+Y}{\|u\|_X}=\inf_{y \in Y}{\|x+y\|_X}.$$
Then by definition of the quotient norm for any $X_n \in X/Y$ there exists $x_n \in X_n$ such that
$$\|x_n\|_{X} \leq \|X_n\|_{X/Y}+2^{-n}.$$
Then we have that $\sum_{n \in \mathbb{N}}{\|x_n\|_{X}} < \infty$ and hence is absolutely convergent and therefore $\exists x \in X$ such that $x=\sum_{n \in \mathbb{N}}{x_n}$. Note this follows from the fact that $X$ is a Banach space.
Now, define $X=x+Y$ and $S_k=\sum_{n=1}^{k}{x_n}+Y$. Now, note that
$$\|U-V\|_{X/Y}=\inf_{k \in (u-v)+Y}{\|k\|_{X}} = \inf_{y \in Y}{\|(u-v)+y\|_{X}} \leq \inf_{y \in Y}{ \|u-v\|+\|y\|}$$
and lastly, we note that $y=0 \in Y$ and hence we have the right most term is equal to $\|u-v\|_{X}$. Hence, we get that
$$\|X-S_k\|_{X/Y} \leq \|x-s_k\|_{X} \underset{k \to \infty}{\longrightarrow} 0,$$
where $s_k=\sum_{n=1}^{k}{x_n}$. Hence, we have that our series in our factor space is convergent and thus $X/Y$ is Banach
Per my comment below:
You can also do this by noting that Given a closed subspace $Y \subset X$,
$X/Y \simeq Y^{\perp}$ and the result follows trivially.
Comment: Thanks for the help, yes, I know, under the hypothesis it is easy to see that $H/M$ is Banach, but, one question, the norm about the quotient defines an internal product?
Comment: You tell me. Do you know how to check?
Another way you could do this is recall the decomposition theorem, namely given a closed subspace of H $ = Y \oplus Y^{\perp}$ then you can conclude that $H/Y \simeq Y^{\perp}$. Then it follows trivially.
Comment: you're right, it's more easy from the theorem of the descomposition, thanks a lot.


How do you heal Mental Stress?

Question: Does the Recovery power only heal physical stress and not mental? Is there a way to heal mental stress besides taking a consequence?
Comment: what's the wording for the Recovery power?
Answer: All stress tracks (not just Mental) clear after a conflict ends. Unless you take consequences, which don't "heal" stress, but more absorb it, all your stress returns as soon as the conflict ends, as long as there's a reasonable opportunity to stop and take a breather.
It is possible to dive right from one conflict to another without a chance to rest. Just defeating a bad guy or whatever is not enough to trigger stress recovery. When wizards in my game are going from conflict to conflict with short rests, I try to decide if they have had enough time to unwind in between. I ask myself, "Is this next conflict a continuous event emotionally? Has there been another state of mind in between?"
I will have to check my book for the exact details on the Recovery power, but if memory serves, it's about Physical attributes, like Toughness and Might are.
Comment: @RP21 - The circumstances under which I would allow a wizard to have a mental consequence healed by magic are practically nonexistent. Consequences take time to recover from. When I say to a player, "You could cast that spell if you take a consequence..." I'm asking, "How much is it worth to you?" I'm presenting an interesting, meaningful choice to player and character both. Take that away and it's just...flat.
Comment: Thanks!! How about healing consequences of the mental kind? like taking a mild for casting a boosted spell, can the Thaumaturgy Spell Reiki Healing Spell on page 300 heal it before we go to a new scene?

How do you heal Mental Stress?


Representation of the Majorana Fermion

Question: In Schwartz's QFT, in the Weyl basis, Majorana fermions are written on the same footing as Dirac fermions, as matrix
$$
\psi_{Majorana}=(\psi_L \quad i\sigma_2\psi_L^*)^T
$$
I don't understand the reason behind this combination. One reason is given, $\sigma_2\psi_L^*$ transforms like $\psi_R$, but how to prove this? This $i\gamma^2$ can be said as the charge conjugation operator. I understand it is real in the Weyl basis but is the charge conjugation operator necessarily real?
Answer: Hint: if
$$
U=\left(\matrix{a^*&-b\cr b^* &a}\right) \in {\rm SU}(2)
$$ and $T= i\sigma_2$, then $T^{-1}UT= U^*$ where $U^*$ is the matrix with its entries complex-conjugated.

Representation of the Majorana Fermion


LNK 2019:Unresolved External Symbol Error in VS 2010

Question: I am receiving the LNK 2019 error in VS2010 while trying to build the project.I have included the header files from other project using external dependencies.Each time at build time the LNK 2019 rises for the function defined in those header files.Any idea how to fix it?
Answer: This error is caused by the linker which cannot find call address of an external function. So it "doesn't know" where is located the implementation of the function declared in your external header file.
To fix this apart from specifying external header files you should also specify the paths to the binary files (".dll" in your case)  built from your external project sources. In order to do this use context menu of your project in Visual Studio - {Properties -> Configuration Properties -> Linker -> General}, then add to the "Additional Library Directories" field paths to the directory where your extenal libraries located. After that use {Properties -> Configuration Properties -> Linker -> Input} and add to the "Additional Dependencies" field names of your external libraries ".lib" files.
This should help.


Interpolation and extrapolation of Discount factors

Question: We are sourcing the discount factors for various currencies. What is the best interpolation method for dates between and out of the dates provided in the factors? Shall I go for flat forward or cubic spline? Please suggest if any other is better.
Answer: Be careful with various naive smooth interpolations of discount factors that are easy to screw up and may lead to unrealistic rates between the nodes.
But your choice depends on your planed usage.
If it's intended to calculate risk, and then hedges based on these risk calculations, then: definitely flat forwards to interpolate between nodes. Use the last observable forward to extrapolate past the last node. Whatever inaccuracies you introduce may not matter much because you intend to be flat IR risk.
Comment: For just mark to market (and maybe under risk scenarios), simple flat forward is fine. Curve smoothing is too easy to get wrong.
Comment: Thanks for response. I don't want to use for trading but only for MTM of option trades to find BSM price.
Comment: Thanks a lot for quick guidance.


Is 'color' countable?

Question: In the Collins, the word "color" itself is countable. In one article which talks about countable and uncountable, the author says "colors" is uncountable. I think the "colors" in the article means specific color such as red, yellow. These words are uncountable.
Here comes my question. If I want to ask what's the color of two dogs, Which one is right, color or colors?
Please help.
Comment: If one were to say "The words brought color to her face", "color" would be used as an uncountable.  Ie, the plural would be "The words brought color to their faces."
Comment: I can't find a marking of the word _color/colour_ as either countable or non-countable in the [Collins English Dictionary – Complete and Unabridged, 12th Edition 2014](http://www.thefreedictionary.com/colour). It would be best to link to the dictionary you used (or cite it) and give the quote.  [Macmillan](http://www.macmillandictionary.com/dictionary/british/colour_1) on the other hand gives a far more detailed analysis of the usages. But MorganFR's answer is perfectly tailored to fit your question, and shows that it's usages, not nouns, that are count or non-count.
Comment: I made a big mistake! Yesterday, I looked up the word via an APP which is a translated edition of Collins.  I thought I got the whole idea about the word. Just now I took your advice and realized the APP doesn't keep the whole content. :(  I'll never use that APP again.  Thank you, Edwin Ashworth. Without you, who knows when I gonna find this.
Answer:
"What is the color of those two dogs?"

Both dogs have the same color.

"What color are those two dogs?"

Both can have a different color, but most likely one color each.

"What colors are those two dogs?"

Both dogs may have the same colors or different colors, but they have several colors each, or at least one of them does.

"What are the colors of those two dogs?"

Both dogs can have the same multiple colors or each be of (a) different color(s).

"Leaves are different shades of brown and red in the fall."
"The reds and browns of the woods in the fall."

As for the names of the colors themselves, they can be countable and uncountable. To differentiate them, you can use "shades" for instance.

Is 'color' countable?


List members of organisation belonging to sub-types

Question: I have my organisation split between local sport clubs.
I'm looking for a best way to list all members of particular clubs - should I use Drupal Views or Civi search'es or reports?
Thnx
R.
Answer: Searchkit looks like it can pull in related contact data
Search view that shows the mutual relationships between two contacts
There's a bit of a learning curve, but I found this overview from a recent CiviCRM meetup really helpful
https://youtu.be/-YJyRt02vvw
Answer: Partly depends who needs to see the report but we tend to build all such results in Drupal Views.
Comment: Hi Pete,
Right now I want to list all members, which is fine, almost - my view doesn't show the club they are member of, even though they are in relationship with the club in their contact panel.
Also, I've got trouble building a filter to show a dropdown of all clubs so the list can be limited.
Thnx
Comment: using views 'relationships' you should be able to join to the required tables and get the required. v overdue reply. apologies


jQuery flot graph is not converted by tcpdf

Question: I Used Flot graph to create the graph. When I try to export the graph into pdf or print. The graph I plotted is not rendering is there any other solution to print graph drawn by flot.
Answer: I can't comment on you question, so I'll ask here:
How does your export code look like?
I use GFlot (Google Web Toolkit wrapper for Flot) together with the CanvasText plugin at http://lessaworld.com/projects/flotCanvasText/ to render text and data onto my charts.
Have a look at this example that generates an image:
http://lessaworld.com/projects/flotCanvasText/flotCanvasTextExample2.html
You can then try to print/PDF the image.
I hope this is useful.


PID tuning help

Question: I'm currently working on a self-balancing robot with an Arduino Uno and a 10DOF ADXL345 sensor. Everything is going fine until I got to this PID tuning part. I've read about it several times but I'm unable to get the desired results. Can somebody give a detailed guide on PID tuning? Thank you.
Comment: How tall is it? How fast do the measurements and adjustments have to happen to keep things from falling down? How fast are they happening?  Where is the code?
Answer: Maybe you can help yourself with this tutorial for PID line follower robot. I successfully tuned my PID for line following and had some success with PID for wall following with sonar.
Comment: Thanks. Let me try it first. I'll tell you when it works :)
Comment: That tutorial looks pretty good.  One difference from most discussions and usages of the normal Arduino PID control is that it focuses on error by putting the setpoint outside the PID algorithm as "Tp", so you can use the arduino PID like this if you do those calcs outside. And "I just take the maximum value we want to send to the motor's power control (100) and divide by the maximum useable error value. For our line following robot we've assumed the maximum error is 5 so our guess at Kp is 100/5=20. When the error is +5 the motor's power will swing by 100 units." is the crux of PID tuning.
Comment: Thanks man. Didn't get the desired results yet but I'm a lot closer now. The robot is much more stable now. Thanks man
Answer: In real life there is no set equation to find the PID values. At best you'll get close with equations and then need to tune the parameters.
For anyone into PID loops have a read of this.
I've found it to be excellent.
My advice is to:

only use P
set I & D to 0
get it and good as you can by trial and error
add I and trial it too

D is for experts really and may cause weird/undesirable jitter.

PID tuning help


Finding Sylow p-subgroups

Question: I am trying some examples of finding Sylow p-subgroups in specific groups and looking for the most efficient way to do so. For example, lets say we need to find Sylow-3 subgroups in $A_4$ and $D_6$, dihedral group of order 12. Using sylow theorems I found there can be only $1,4$ sylow 3-subgroups in group of order 12. But how do we actually find these subgroups? Since these groups are of small order maybe check the orders of each element might work but this is not the best way. Are there any tricks or theorems out there to find the subgroups?
Answer: In both $A_4$ and $D_6$, the Sylow 3-subgroups are of order $3$ (the largest power of $3$ that divides the group order $12$), hence cyclic.  So finding one such subgroup amounts to finding an element of order $3$ in the group, which you can do by inspection.  And once you've got one Sylow 3-subgroup, you can find all the others (if there are others) because they're conjugates of the one you've got (or you can just check for more elements of order $3$).

Finding Sylow p-subgroups


Work done by a varying angle

Question: I know that work done by a constant force is $W=\vec{F}\cdot \vec{x}$, and that work done by a variable force is $\int \vec{F} d\vec{x}$. However, how do you calculate work done by a varying angle?
Comment: Are you sure you don't mean *torque*?  Torques & angles are analogous to forces and distances, in that order.
Answer: Indeed, it is the same formula.
$$W=\int_C \vec{F}\cdot d\vec{x} $$
Check that this is the same as
$$\int_C |\vec{F}|\cdot \cos(\alpha)\cdot dx $$
This integral is a path integral, that means that you're summing all the contributions along all the tiny portions of the path of your trajectory.
Both $F$ or the angle can vary along the path. Anythin inside the integral can.
Answer: There is a difference between $\int Fdx$ and $\int \vec{F}.d\vec{x}$.Basically a difference of dot product which is capable of calculating work by a variable angle.

Work done by a varying angle


Why do I keep timing out on Minecraft multiplayer servers?

Question: Whenever I join a multiplayer server I get to play for around five minutes, it loads the chunk and lets me interact with furnaces, ect. but after some time it disconnects me and says 'Timed Out', my friends don't get disconnected to the server though. When I check my internet it says I'm connected. What's going on?
Comment: If you're having general internet issues, try asking on [SuperUser](http://superuser.com/). They're better at tech support than Arqade (we focus more on playing games).
Comment: Does this only happen with a specific server or all servers?
Comment: All multiplayer servers
Comment: How reliable is your connection otherwise? Have you played other online games with it?
Comment: It's pretty unreliable, it disconnects me a lot and goes on limited, I play Sims 4, which doesn't need internet connection, but you can use internet and it disconnects there also. However, when I get disconnected from a server my internet usually is connected.
Answer: I have similar problems with my own router. Unfortunately, a lot of it is due to high Internet usage from the rest of my family and a low available connection. (The only service available in my area is 3 Mbps.)
I would guess the problem is not with your router, but with your internet provider. Check which speed you currently have and see if faster services are available if you are willing to pay more.
Otherwise, others in your house using streaming services like Netflix or Pandora will GREATLY increase the issues with connection. If you can plug an Ethernet cable directly into the device you are using, this may help increase reliability.
Answer: As you said in a comment, your connection is very unreliable. As a result, you will have trouble playing any Internet-based game, not just Minecraft, because packets are lost every time you lose connection to the Internet.
The most frequent cause of intermittent outages can be traced to your router or modem, which is very often supplied by your ISP. If you are certain that it is not your router, you should contact your ISP and ask them to diagnose or replace your modem.


How can I stop my cat from removing her cone?

Question: I just got my cat back from being spayed.  She's got the stitches, and she's supposed to wear the cone for a week to stop her from licking them.  Problem is, we've gotten the cone on her four times now, and she's managed to pull it off all four times.
I really don't want to hurt her, and I know she doesn't like the cone at all.  I have to go to work, so I can't supervise her 24/7 to stop her from licking.  But how can I make sure she can't take the cone off at all?
Comment: Related (for dogs): [What can I do when the cone of shame is too heavy?](http://pets.stackexchange.com/questions/6438/what-can-i-do-when-the-cone-of-shame-is-too-heavy)
Answer: There are a few options. Usually when the veternarian supplies cones, they are hard plastic and annoying to the cat because they interrupt peripheral vision and hearing, as well as eating and drinking.
There are soft cones available that some pets find more tolerable, Trimline is one manufacturer. These cones can be worn in the traditional "up around the head" fashion, or turned down to form a bell around the body. Some cats find the turned down position tolerable because it doesn't interfere with vision/hearing.  If you get one of these collars and try the turned down position, I recommend using it while you can observe your cat to make sure that she cannot reach the stitches with the cone in this position.
Another option is a protective shirt. There are commercially available options, but you probably don't want to wait for shipping since your cat has already had the surgery. You can make a similar shirt at home.
Basically, take an old T-shirt and cut four holes in it for the cats legs. Then wrap the shirt around the cat and pin/sew it closed at/near the cat's spine. You don't want any seams near the wound/suture (belly), that should be a smooth flat piece of fabric. The shirt should be snug so your cat cannot wiggle out of it, but not so tight that it cuts off circulation. You should check the wound every 8 hours or so while it's covered, and monitor your cat when you first put on the shirt to make sure she doesn't get tangled in it.
If she licks the shirt it should be alright, but if she bites it you'll want to reinforce it with thicker fabric (like denim) over the area with the stitches.  The fabric will likely stretch and wiggle, that's normal. Just repin it as necessary to keep the shirt on and covering the sutures.
Comment: @MattS. a cat costume may not have the required coverage on the belly, and/or may not be tight enough. But you could get lucky I suppose.
Comment: No need to make a shirt this close to halloween, run out and buy a cat costume! :P
Answer: I have a large (strong) grown up cat, who've had a major operation on his hind quarters, and needed a hard plastic cone to keep him from biting the stitches.
To keep him from pulling the cone off, I tied a long ribbon (actually a bandage) through the loops in the cone, once around his neck, crossing down on his chest - behind the front legs - and crossing once more on his back, before connecting to the loops in the cone again. Then it is neatly tied with a bow on his back.
It isn't super important exactly how you tie it - just keep it behind the front legs and cross onto the back. That way, when the cat tries to pull it off, it will pull against his front legs, and the cat will stop pulling.
This is a sketch of how the ribbon could run:

The red and blue are both ends of the same string - they start at the middle, just behind the head of the cat - and run across the breast and under the front legs. Then somehow they are tied together on the back of the cat. It doesn't matter exactly how they connect at the back, but I like to run them once more through one of the loops on the cone.
Technically it would still be possible to pull the legs out of the loops, and pull of the cone, but so far my cat hasn't figured that out.
Answer: I too had the problem of my cat Fonzie (now nicknamed "Houdini") pushing the cone off his little head.  What I did works great I used a halter and attached two loops of the cone to the halter on his back and the one front loop to the part where the halter sits on his chest. It is a halter one would use with a leash on to take the cat for a walk. He isn't happy and I wish I could make him understand it is temporary and for his own good. Love my cats so much and one can never say cats aren't smart.
Answer: my two cats were just spayed & neutered. What I did to keep the cone on was took the ribbon out that the vet supplied and put the collars they already wore in place. It worked like a charm. They were never able to get it off because they couldn't untie the ribbon (:
Answer: I visited 4 vets when I was about to neuter my cat. Only one of them recommended a cone after the procedure. The rest said it's very unlikely she will lick or nibble on the stitches, and in the rare case she does, we will deal with it then, as it is also unlikely she will be able to do irreversible damage before I notice it.
I also know that most vets do some plastic surgery on top of the stitches, so they are less obvious and less accessible. Do ask the vet if he includes that in the operation.
I ended up not using a cone (and sticking with one of the vets who were against it, for other reasons), and she never even tried to access the stitched area before it healed. Of my dozen or so cat-owner friends, none of them has used a cone and none of their cats licked or touched the stitches.
I'm just letting you know that the cone is an option.
Perhaps a good thing to discuss with your vet is whether it's possible for the cat to do considerable damage to the stitches within the time you are away. If not, and you decide against the cone, you will always be able to check on her when you're back home, and call the vet in the unlikely chance something is wrong.


Magento 2: changes made on one store must be apply to default store too

Question: When you edit a product on the All Store View scope it applies the changes to all the stores. I want the reverse of it like if I made changes to a different store then that change must be applied to default or all stores. i.e if I disable an image for store 1 it should be must be disabled for every other store too.
Answer: This is dependent on the scope of an attribute. If an attribute's scope is global, and you change the value of an attribute in any store, then that change will be applied globally, i.e. to all the other stores.
You can change the scope of an attribute to global in Stores -> Attributes -> Select an attribute -> Open the attribute -> Advanced Attribute Properties
If we consider image attribute, I think it is set to store view scope by default. You can try changing it to global scope and it should work.


Ways to get faster times Quantum Conundrum?

Question: I'm trying to get the speed times in Quantum Conundrum and can't seem get any faster is there any way to move faster or to skip the speeches to move faster?
Comment: Any reason behind the down vote?
Comment: My bet is due to the fact that your question is a little open ended.  Is there a specific level you are having trouble getting faster times on?  What have you tried doing to decrease your times?
Comment: I am currently working on the first few levels including the one that requires no shifts what so ever.  I have tried cutting corners  jumping items in the way standing in front of the doors to new rooms while waiting for speeches to end. I have not figured out Run if there is a function for this.
Answer: I know it's only going to be marginally useful, but there are only best practices that I can provide rather than concrete answers to so open-ended a question. Even if you had specified which levels, should the levels in question either take shift control out of your hands or lack shifting altogether, it all comes down to your FPS platformer navigation skills.
General Strategies

There is no "run". You can only walk at one speed really, but the use of strafing can possibly help speed up your movement - if forward movement and sideways movement are equal, diagonal movement, using them together at a diagonal would be faster (think of a square representing movement speed), but I haven't confirmed whether this is the case, even though it would appear true from my own goal time runs. Jumping seems to be slower than walking so jump only when necessary.
Speech progresses on its own. It is usually triggered by passing through an invisible trigger volume in the level or performing some specific trigger interaction and will be skipped when another speech segment commences. To speed up segments dependent upon waiting for some speech, quickly reach the triggers to begin the speech as early as possible.
Learn the area and map out the shortest route, cutting every corner as short as possible and jumping as little as possible. Remember that a straight line is the shortest distance, but also avoid clipping on furniture or corners as that can ruin a high speed run immediately. Always look for shortcuts to avoid whole areas or certain actions and believe me when I say that there are many shortcuts, but that some of them require a high degree of precision.
Once you are confident you've learned the level and are taking the correct approach, quickly restart the level as soon as you screw up any given attempt to avoid wasting time on a failed attempt. You will be doing a lot of this.

Shifting Strategies

When you can't control the shifting, learn Desmond's timing and take risks, rushing to make use of every shift to the fullest of your ability for the duration of the shift. Some of these can be infuriatingly tight, but are necessary for some of the goal times.
While sometimes fewest shifts can be synonymous with goal time, often they tend to be objectives in opposition to one another. Do not be afraid to shift as much as necessary to get the goal time and worry about shift goals for another run.
There are several stock shift maneuvers that the game has you perform that you should learn and learn well. Quickly fluffy+slow throwing projectiles for you to ride or catch elsewhere in the level; Upside-down/normal surfing/catapult/projectile levitation, especially timing to maintain momentum; Quick fluffy+heavy throwing projectiles through glass; Upside-down+slowing objects for you to hop across; Shifting mid-jump to let things fall or raise as needed.
Don't be afraid to skip sections even if the speech tells you you will need to do it. It may be harder without going through a certain section here or there, but it will invariably save you time.

If you have questions about specific levels, feel free to create questions for them and I will answer as best I can as I've gotten the goal times and shift goals on every level.


Is using i++ (or ++i) really a good practice?

Question: I know the differences between i++ and ++i (like this) if I want to use their new values. And I saw many examples in The C Programming Language (K&R) use expressions like s[i++] = c;. Sometimes, I come across codes (shown following) make me confused and this style seems highly regraded by them.
while (*string1++ = *string2++); //in c

And in this post, Jon 'avoid using' this style.
So my question is to use i++ (or ++i) like above code a good practice? If not, in which situation should I use it (Just when I don't use its new valve ?)
Comment: when it makes your code more readable.
Comment: It depends on the specific example you take in consideration. Your example is clear enough.
Comment: sometimes `i++` make code more readable compare to `i = i + 1`, then you can use it. but not always e.g. don't do `j = i++ + k++`.
Comment: @BryanChen Do you mean using i++ is to make code more readable?
Comment: When you can, use the prefix operator. Using the postfix operator might result in a performance penalty in some cases.
Answer: By itself, i++ is a clear, idiomatic expression for the idea of incrementing a variable. By itself, it is as clear as it gets. A computer language was named after this idiom (C++).
Jon wasn't saying to avoid "i++"; he was saying to avoid combining it with other expressions that would complicate things, where the increment operation was a "side effect". Like:
arr2[++j] = arr[++i];   // now what the heck is going on? I have to stop and look.

In that case, it is more reasonable to avoid it, and I agree with him. As you start to tweak code, and move things around, or add logic, the increment might go away, move, become redundant etc. and it is often better to perform the increment on a line by itself, or in a loop header instead.
The interesting thing about the ++ operator, besides that it Was a genius idea, is that the prefix and postfix alternatives encode more than just "i = i + 1", they encode an additional evaluation of the left or right hand side of the assignment, so to speak. (Or you could think of it as pre/post evaluation).
So ++i is functionally:
i = i + 1; return i

and i++ is functionally:
temp = i; i = i + 1; return temp

This difference causes additional "trouble" by hiding bugs, and you can see why, if the compiler doesn't optimize the generated code, they have different performance ramifications.
Answer: It seems to largely be a matter of personal style and the requirements of the situation.
It's more concise to write i++ compared to i+=1 or i=i+1, and it can help you to remove lines of code that don't communicate an essential fact of the algorithm.
Of course, Jon Skeet is right (as usual) that it can make your code more difficult to understand: mentally distinguishing between ++i and i++ is another cycle your brain has to go through to understand what's going on.
There are situations where more granularity in your code is what you want; there are times when you don't care as much. There aren't really any hard-and-fast rules.
Of course, having said that, I would personally recommend not using i++ or ++i as function arguments (i.e. foo(i++)), since that can introduce some very hard-to-track bugs if you're not very careful, or mixing them with other operators (i.e. Bryan Chen's example of i++ + k++).


Notify Requestor when Case Status Changes

Question: I'm trying to figure out how to notify the requestor when the Case status changes. For e.g. New to Inprogress with comments.
Comment: A workflow email alert maybe?
Comment: Workflow Is used but unfortunately, it's not firing if I use evaluate the rule created, and every time it's edited but if I use created, and any time it's edited to subsequently meet criteria. It constantly trigger every changes made. Can something be done
Answer: you can try something like below :

Create a Workflow Rule.
Evaluation Criteria : Everytime the record is created or editted
Workflow Criteria : PRIORVALUE(Status) != Status

Add your email alert in action. This should work.
thanks,
Answer: There are multiple ways to do this

You can write a workflow on case object. I am not sure about the workflow but the trigger always work.
You can write a trigger on that object. The trigger should be on update. When the status is changed you can send an email to requester.


Black line/stripe on my camera

Question: I was taking some pictures on my camera a Nikon-D3100 when I noticed a black line appearing at the top of the photos, doing a bit of research I thought it might be a problem with the shutter, could someone help me confirm if that's the problem?
As you an see I am not a professional photographer I would really appreciate any help
Comment: Were you using a flash during that photo? Was there another light source (such as a ceiling light)? If so, what was the bulb (incandescent, fluorescent, LED, ...)?
Comment: Considering the age of your camera, has it been heavily used? Regularly used? Has it sat around for a long time?
Comment: Is the image on the back of the camera a preview image of a still photo you have taken? Or the Live View feed with the camera set up to shoot video?
Answer: That result is characteristic of using a shutter speed that is too fast with flash, and manual mode will allow you to do this.
The flash sync speed for the D3100 is 1/200 and no faster. If the flash is off camera you may have to use a slower shutter speed than max x-sync in order to allow for some communication delay (but the exposed part looks like on-camera flash, so probably not an issue).
Edit: given the latest comment there is a physical obstruction in the way of the sensor. Take the lens off and I suspect you will find a stuck/broken shutter curtain.
Comment: The example image shows a Tv of 1/10 used for the example shot. That's considerably longer than 1/200. It may be a sync issue, but if so it is not due to a Tv shorter than the camera's X-sync Tv, but rather a timing issue.
Comment: @MichaelC, it also shows live view video/audio recording along with picture settings (L/NORM)... I assume it is not image review data (I've never seen that display configuration before). I considered the possibility that this was video and the only thing I could come up with is a hanging mirror... but I believe that would obstruct the top of the sensor/bottom of image.  And if it was not a flash image but video feed, I would expect the exposure to be much more even, especially at f/7.1 (no vignetting).
Comment: I still get the same result, the problem persists with any shutter setting with or without flash, the line also appears in the live preview before taking the photo or video.
Comment: @user99045 then there is a physical obstruction. Take the lens off and I suspect you will find a stuck shutter curtain.
Comment: Yeah, only the upper curtain is moving, the lower one is stuck, what you recommend?
Comment: you can try to knock it loose, but that's likely to be a temporary fix at best. I suspect it is not cost effective to repair.

Black line/stripe on my camera


Is the Traveler the same entity in all timelines?

Question: Is The Traveler Capable of time travel? And if so are they the same entity no matter what timeline you are in?
Or are they limited to a specific timeline?
Comment: He was in three episodes, in fact: Where No One Has Gone Before, Remember Me, and Journey's End. Additionally, he's appeared in some short stories, but I'm not sure on the policy here with Star Trek EU, so I wouldn't cite those.
Comment: Excellent question.
Comment: It is not very clear what you are asking here; can you provide a little more context and better explain your question?
Comment: I only recall the traveler being in one episode of TNG. Was he in any other episodes or movies or other media? I wonder if the lack of response to this question may be due to the traveler not having been in much star trek media. Perhaps the OP should document where he has seen mention of the traveler so that the question can be more clearly framed.
Comment: Perhaps Memory Beta may contain relevant citations, as it did for @Olivee_C's answer to this [other question](https://movies.stackexchange.com/questions/4137/what-happens-to-wesley-crusher-when-he-leaves-with-the-traveler#).
Answer: The Traveler is indeed capable of time travel, or at least, what the Traveller does is, from his point of view, equivalent with time travel in a human perspective:

RIKER: You are from a different time, aren't you?
TRAVELER: Well,
no, not exactly from another time. Although as you understand the
concept, yes, perhaps that term fits as well as any.
s1e06 Where No One Has Gone Before

When they are at the edge of reality, Picard also seems to feel that they have travelled through time as well as space:

Captain's log. Any time entry is meaningless.
s1e06 Where No One Has Gone Before

Additionally, the Traveler's abilities manipulate energy and time via thought:

TRAVELER: Such musical genius I saw in one of your ship's libraries. One called Mozart, who as a small child wrote astonishing symphonies. A genius who made music not only to be heard, but seen and felt beyond the understanding, the ability of others. Wesley is such a person. Not with music, but with the equally lovely intricacies of time, energy, propulsion. and the instruments of this vessel which allow all that to be played. You're right, I must hurry now. But you're right in something else. He is just a boy for now. He should be encouraged, but told none of this.
...
TRAVELER: I have the ability to act like a lens which focuses thought.
s1e06 Where No One Has Gone Before

However, as an entity, he does seem to be bound to a singular timeline. In the tremendously existentially terrifying episode "Remember Me", when Beverly is trapped in an alternate reality, the Traveler helps Wesley rescue her. They use specifically Starfleet means of manipulating warpfields to rescue her, and the Traveler never hops over to her reality to explain what's going on. Of course, Wesley uses his latent Traveler powers to be able to find the right alignment and "see beyond the numbers", but this doesn't imply that he could, of his own volition, skip between dimensions.
For less canon sources, I recommend "Gods, Fate, and Fractals" by William Leisner, in which Wesley screws up the time stream by removing the Maquis from reality, and the Traveler promises to fix the problem.
Comment: Outstanding answer, thank you very much. This answers my question perfectly.


Enterprise find files (via powershell) exclude Tempory Internet Files

Question: I am trying to run this command via powershell on every computer on my network.
I am running into a problem with Temporary Internet Files, providing too many false positives.
Can anyone suggest a way to improve this command?
dir C:\Users\ /S /B | findstr /i "".t.st."" > "C:\test.txt"

One suggestion, was
dir C:\Users\ /S /B | findstr /i "".t.st."" > "C:\test.txt"
dir C:\Users\ /S /B | findstr /i "".t.st."" | findstr ""Temporary Internet Files"" > "C:\test2.txt"
fc C:\test.txt C:\test2.txt > C:\results.txt

But running through tests, it didn't give me the results I was looking for. I still had duplications. Or it would say the files are too different.
Thanks!
Answer: If you are running this through PowerShell then why not use PowerShell commands? Your examples are using the legacy DIR command. You could use Get-ChildItem instead. You can use -Exclude to skip a folder. You could use -filter or -include to find the files you want. Worse case is to get the files and then pipe to where object perhaps using a regex pattern to filter out the files you want. I can't tell from your commands what files you are looking for.
Comment: get-childitem c:\users -recurse -exclude "\Temporary Internet Files"


What are the pros and cons of cast iron vs. porcelain covered steel bathtubs?

Question: What are the pros and cons of cast iron vs. porcelain covered steel bathtubs?  I'm wanting a free standing bathtub but do not want the fiberglass or acrylic type that are common now.
Comment: I do not think anyone is manufacturing pressed steel free-standing tubs. What do you have against acrylic? There are many options available, many colors, new lightweight and eco-friendly types, etc.
Answer: Great call. Cast Iron's bottom & sides are solid, none others are. Steel is quite bouncy & hollow sounding. Cast Iron is very heavy so consider that if you'll be installing yourself. You'll want 3 other helpers & to make a stretcher under its rim out of 2x4's & treat it like a King or Queen...unless winding stairs or shallow hallways will be a length issue.
Answer: Claw foot tubs cost more than modern steel tubs by about one order of magnitude, but you sure do get what you pay for.
A cast iron tub will survive being removed and installed multiple times, whereas a steel one might need to be replaced in your lifetime. They're ~$150, why would you ever reuse an old and abused steel tub?
A used and slightly abused claw foot tub is worth repairing however, if it ever becomes damaged, and should serve you well until the end of your days. Provided, you never chip the enamel and don't use any incorrect cleaning products on it. This applies to both types, but cast iron tubs are much more tolerant of abrasive abuse and impacts, as they generally have a thicker coating of enamel.
Answer: steel is flexible and i have never actually seen a freestanding steel tub (i would be interested if you have).  it typically is stronger than cast iron, so its made in thinner sections.  steel tends to continue rusting, whereas iron tends to passivate and slow or stop rusting once it has an oxide layer.
cast iron is readily available, but its a porous material that is intrinsically brittle. it tends to be a heavier section than steel, so its correspondingly heavier as a tub.
both corrode, and both are heavy.  you have to ensure the coating (porcelain, enamel or urethane) have to be kept intact.  patch or wax at first sign of a chip or crack
steel tubs are easier to get into place.  cast iron tubs are brutally heavy and can actually require floor and stair reinforcement just to get them into place.