rt.representation theory – A characterization of reflections on the Euclidean space

In the book "Introduction to the algebras of lies and the theory of representation" by J. Humphreys, page 42, the author demonstrates the following motto. Leave $ E $ be a Euclidean space of finite dimension on $ mathbb R $ Y $ mathbb phi subseteq E $ be such that $ mathbb phi $ extends $ E. $ Suppose all reflection $ sigma_ alpha $,
$ alpha in mathbb phi $ leaves $ mathbb phi $ invariant. Yes $ sigma in GL (E) $ leaves $ mathbb phi $ invariant, promptly fix a hyperplane $ P $ and send a zero $ alpha $ to $ – , $ so $ sigma $ it's just the reflection $ sigma_ alpha $ around the hyperplane $ P. $ $ sigma_ alpha $ is defined as $ sigma_ alpha ( beta): = beta- frac {2 langle beta, alpha rangle} { langle alpha, alpha rangle} alpha. $

He argues that or $ tau: = sigma sigma_ alpha ^ {- 1}, $ $ tau mathbb phi = mathbb phi. $ As is true It is true that $ sigma mathbb phi subseteq mathbb phi $ implies that $ sigma mathbb phi = mathbb phi $? Also how to prove the rest of the motto?

Naiwen's reflections

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co.combinatorics – Circular permutations (bracelets) with similar things (reflections are equivalent) using the enumeration of polia

The circular permutations of N objects of n1 are identical of one type, n2 are identical of another type and so on, so that n1 + n2 + n3 + ….. = N?
There is a similar question but it does not address the case in which the reflections are under the same equivalent class.$$ frac {1} {N} sum_ {d | N} phi (d) p_d ^ {N / d} $$ This is when the reflections are not the same. How does the equation change under this new restriction?

Note: I could not comment on that question because of my low reputation, so I asked this question.

Reflections on this new Democratic Party that supports and defends socialist views and policies?

Many young people today have the feeling that capitalism has failed. For generations now, capitalism was promoted as the best system because it raises the standard of living. But our standard of living has been slowly declining for 40 years, more than most Americans have ever been alive!

Personally, I do not think capitalism is the problem, it's the way we DO capitalism. I call it "American style capitalism", but others call it "advanced stage capitalism". or even & # 39; final stage capitalism & # 39;

The leadership of the Democratic Party, the mainstream, remains anti-socialist. They have to enrich their sponsors to maintain their power, just as republicans do.

The Democratic Party desperately depends on the crowd of less than 30 years. These are the people who have been most affected by the current system. They have taken a page from the REPUBLICAN manual, the idea that you get people's votes by convincing them that the system puts them at a disadvantage. These are the people who want the government. to provide (or make available) the service they desperately need: medical attention, perhaps childcare, workers' rights, etc.

Remember also that Republicans use the word "socialism" for anything they do not like. EVERY Democratic candidate will be called "socialist", so the Democrats have an interest in making socialism no longer a Republican "word of fear".


autofocus: Is it possible that MF with focus peaks and contrast-based AF are likely to be fooled by metallic reflections?

He wondered about some shots that went wrong, that were taken with a peak of focus and a manual focus, and whether there were metallic / reflective mirror reflections (think of scenes with wrinkled auto accidents or broken glass in the clear midday sun). Or reflections in the water).

Will a peak focus system easily detect virtual images in reflective objects and suggest an approach that is outside of what would be correct for the reflective object itself? Is this a concern to take into account with the automatic CDAF approach as well?

Reflections on: Server operating system

This is my last in a 4 part series. I went with a dedicated server at OVH. This allows me to install a variety of operating systems and control panels. I think I'll go with Plesk or maybe cPanel (and domain registration through CloudFlare). I will be running a dozen or more web domains, some more subdomains. I will have some instances of WordPress using MySQL and PHP. I will be the only administrator.

I can reinstall it at any time, but I would like to not have to do it once the development starts. To prove things, I went with:

Linux Plesk Onyx (Debian 9 "Stretch") – debian9-plesk17 – 64 bit

I made this decision based solely on the fact that my current dedicated server in Ionos is Debian 8 and I thought that 9 is 1 better than 8. Apart from the default control panel installed, would you ever notice a difference with any of the following options?

concurrency – Reflections on the definition of disadvantage of concurrent processing?

I am a Computer Science student who is currently learning about concurrent processing. I found that the benefits and disadvantages of my book were vague, I did some research online and put together a more detailed way to define the disadvantage of concurrent processing; Thoughts and corrections are appreciated.

The simultaneous use of processing in several users running the same program means that nobody can finish until everyone has finished. This is inefficient compared to the consecutive processing in which the last user would end at the same time as the last user in the simultaneous processing, but some users would finish significantly earlier. However, the scale of this inefficiency is limited by the number of subprocesses, because simultaneous processing only changes between the first process of each subprocess queue. However, the process at the beginning of each thread can change with the use of interrupts.

Reflections on email "alias" | Web Hosting Talk

I'm working in a small start-up company. And, as you can imagine, money is scarce!

I currently have 3 email addresses that are provided with my VPS.

For security reasons, I am interested in switching to ProtonMail, but unfortunately, they seem a bit expensive for the plan I want.

Currently they offer a "professional" plan that would allow me to have an encrypted email with my own domain name. The problem is that this costs $ 8 / month and they tell me that I would have to pay for a separate user account if I want my 3 email addresses separated.

I would like to have: cat@mycompany.com, support@mycompany.com and sales@mycompany.com

So, for that to happen, I would end up paying $ 96 / year for email account for a total of almost $ 300. (That's a lot of money when I do not even know if my company will survive the first year of business).

So this leads to my question …

The ProtonMail support told me that, instead, I can opt for their "Plus" plan, which would consist of an account (ie, Inbox), but would allow up to 5 email addresses with "aliases".

They are telling me that with the "Plus" account, I could use filters to organize all the emails that arrive to the account and divide them into separate folders. And when I asked about responding to customers, they assured me that by replying to the email with alias it would be filled in the "To:" field, I could reply to an email and make it appear to come from cat @ mycompany. com

Is there any reason why you DO NOT want to opt for this more affordable option that uses aliased email addresses?

My biggest fear is that email servers and spam filtering software, and to a lesser extent, "investigative" clients, can look at the headers of emails and determine that all of these different email addresses actually come from from a single email account, and that in turn puts me on a spam list or loses the trust of the clients because it seems that I am plotting something "suspicious".

What do you think of all this and what do you think I should do?

They have a sale until the end of Friday (tomorrow), and I'm interested in being paid with ProtonMail, but I'm not sure which is the best option?

Thank you,


Reflections on Chrome's plan to distrust Symantec certificates

This has been a theme that has been marking the back of my mind for quite some time.

Amazon uses the Symantec certificate for the product images we show on our site.
And Google is scheduled (April 17, Chrome, update 66) to consider any site that uses Symantec certificates issued before 2016 unsafe.

So, what will really happen when Chrome update 66 starts?
Has Amazon updated its certificates? If so, why do we see the warnings of images-na.ssl-images-amazon in the inspections of our browser?
And what exactly does it mean to "eliminate the trust in certificates issued by Symantec"?
Will our SSL certificates be disabled in Chrome? Site blocked?

I guess Amz has all this covered, right? The Google / Amazon relationship is not one that smells like popery. There is no love lost there …

Any ideas?

Read all the details here …