Is the union of a Banach space under a certain standard?

As a set of sequences, take the union of l ^ p, p> = 1. As p increases, the space l ^ p is larger, with strict inclusion.

However this infinite union is strictly contained in c_0, let us consider
x_n = 1 / ln (n + 1)
therefore the usual norm c_0 will not give a closed space, because c_00 is dense in all l ^ p.

Is there a norm that transforms the union of l ^ p into a Banach space, presumably with dense c_00?

statistics – Deviation of the standard deviation of the weighted sample

According to this Mathworld page, the variance of the sample standard deviation $ s $ can be calculated analytically with eq. (10), assuming a normal distribution.

$$
mathrm {var} (s) = frac {1} {N} bigg (N – 1 – frac {2 Gamma ^ 2 big ( frac {N} {2} big)} { Gamma ^ 2 big ( frac {N-1} {2} big)} bigg) sigma ^ 2
$$

Now what is the variance of the standard deviation of the weighted sample, calculated as the square root of the variance of the weighted sample? Is there an analytical solution for this?

$$
mathrm {var} bigg ( sqrt { sum_ {i = 1} ^ mathrm {N} w_i (x_i – mu) ^ 2} bigg) = ? quad mathrm {, where} quad sum_ {i = 1} ^ mathrm {N} w_i = 1,
$$

I approached a simulated variance if I substituted it $ mathrm {N} $ in (10) with $ frac {1} { sum_ {i = 1} ^ mathrm {N} w_i ^ 2} $, but there is always a bias in the simulation that I cannot describe.

macos – Is it possible to use Thunderbolt networks and standard Ethernet networks simultaneously?

Yes, that is certainly possible – indeed, that is what happens if you connect them like this.

Thunderbolt 3 allows transfer rates up to a theoretically high level of 40 Gbps.

The relative speed depends on the type of Ethernet connection with which you are comparing it. If you're using 10 gigabit Ethernet – you probably won't see any practical benefit from the Thunderbolt 3 connection (if you don't transfer data from disk, you could get huge benefits though). If you are using Gigabit or slow Ethernet, you will see a massive improvement in transfer speeds.

theme – Why use blocks, widgets and LESS when creating standard web pages?

why use blocks, widgets and LESS to create a web page when CRM supports standard web page building?

I'm trying to understand the overall logic and strategy for creating themes and content in the CMS and the front-end. I know little PHP and XML so my goal to use CRM. Sorry if it turns out a little confusing … hence my dilemma.

At this point, I'm not building anything deeper than a website from which I can sell.

  • I built my content in pages without blocks or widgets. Is it a security issue?
  • I am adding to LUMA with the feild, Head> Scripts and Style Sheets in the CMS backend.
  • I use categories for my navigation;

The site works very well!

So, after looking at Magento theme in Dev Docs the other day, I realized that maybe I was using Magento the wrong way.

I ask questions:

  • Why should I use blocks or widgets if I am not starting a business
    enter features for my website?

  • What are the advantages of blocks compared to the simple integration of HTML code in a page, besides deactivation and activation?

  • Why should I add to LUMA with a LESS document when all I have to do is write CSS externally, internally, online or via the CMS frontend via Content> DesignConfiguration> Head > Scripts and Style Sheets field? Is it a security issue?

  • Am I confusing the line between developing Magento2 and creating front-end Magento2 websites?

  • I work in PRODUCTION mode. Is there any reason for me to go into DEVELOPMENT mode since I'm building in CMS?

I know I have asked a lot of questions, but I have been about to use Magento for a year and I still have a lot to learn. At one point, I would like to be a Magento developer, but alas, I'm at the front door of Magento.

Any light you throw on my quest for the enlightenment of Magento2 is more than appreciated. Thank you in advance for your time and professional knowledge.-Starkemp. BTW: Thank you Prince for all of your previous help

Character layout behavior (question on Unicode standard)

I have read the basic specification of Unicode (see https://www.unicode.org/versions/latest/). I mostly understood what the text explained in the section 2.1 Architectural context until he starts talking about layout behaviors. It seems that there is no preface or explanation of the expression "character layout behavior".

Section 2.1 explains how character encoding should be designed with text processes and algorithms in mind, since a choice of encoding can make rendering text and other processes more complex (or more simple, depending on the choice).

The specification then continues with a Identify the character sub-header that uses multiple sentences, including the word "layout". Here are some examples from the text:

  • "Whenever Unicode declares the default character layout behavior, it is made to ensure that users … "
  • "L & # 39; current disposition in an implementation may differ in detail. "
  • "A mathematical layout system, .., will have many domain-specific rules for disposition.. "
  • "The purpose of defining a Unicode defect layout behavior does not consist in applying a unique and specific aesthetic disposition for each script .. "

What does "layout" and / or "character layout behavior" mean in this context?

design – In a tennis scoring program, what would be a good approach to storing and presenting both standard games and tiebreakers?

In a tennis match, each game has the possible Love, 15, 30, 40 or Advantage scores. This could be modeled as a dictionary [0: "Love", 1: "15", 2: "30", 3: "40", 4: "Advantage"] or the type cases listed. In the situation where both players win six games however, the next game is a tiebreaker where the points are simply scored as 0, 1, 2, etc. where the first to 7 with a margin of 2 wins the match. What would be a good approach to take both into account in scoring?

encryption – Would Triple DES-X with 9 keys be much slower than standard Triple DES?

Since a single hardware pass from an XOR with a 64-bit key is very fast, Triple DES-X using nine 64-bit keys used in the following way would be practically identical in terms of code size , memory consumption, and execution speed at 3DES?

XOR (key 1)
DES (key 2)
XOR (key 3)

XOR (key 4)
DES (key 5)
XOR (key 6)

XOR (key 7)
DES (key 8)
XOR (key 9)

In addition, would it be significantly more resistant? Would he still suffer from the same vulnerability based on the block size of DES-X?

gn.g general topology – Positive Borel measurement with empty support on a standard measurable space

Let $ X $ be a $ T_0 $ topological space (no $ T_1 $), and leave $ Sigma_X $ to be the Borel $ sigma $-algebra. Suppose that $ (X, Sigma_X) $ is a standard measurable space, i.e. measurable isomorphic to Borel $ sigma $-algebra $ (Y, Sigma_Y) $ of a complete separable metric space $ Y $.

Question: Is there a positive measure $ mu $ sure $ (X, Sigma_X) $ with empty support, $ mathrm {supp} mu = emptyset $?

Note that the measurable isomorphism between $ X $ and $ Y $ is a priori simply measurable Borel, and can potentially map open sets to sets without interior and vice versa.

Thank you.

Discussion: The question arises of the divergence in the definitions of the support of a Borel measure on a topological space. I think the standard definition is this, in which case, unless $ X $ is a very good space, you should not expect $ mu (X setminus mathrm {supp} mu) = 0 $. However, in Propositiom 8.6.8 in Dixmier "$ C ^ * $-algebras ", the author defines support for a measure as the smallest closed subset with negligible complement (the standard analysis definition). Now I wonder if the two definitions coincide in this context. Note that the space in question is only $ T_0 $ in general, has a locally compact dense open subset (proposition 4.4.5 in the book), and Borel's structure is measurable isomorphic to that of a complete separable metric space (proposition 4.6.1 in the same book ).

user expectations – What is a standard application lexicon?

I am developing a user manual for an application that controls hardware. I need to guide the user through the application to configure it, adjust the parameters and for general use.

What is the standard application lexicon when referring to the interaction of the user with the application?

Here are a few that come to mind …

Touch (A):

Screen (B):

In short, I am trying to say:

To configure this later, _____ (A) the "Skip" button in / at the top right of _____ (B).

Can I return to the UK with a standard visitor visa granted for a job interview

I have applied for and obtained a British Standard Visitor Visa (MULT) valid from October 2019 to April 2020 (6 month validity)

It was for a job interview (company A), I visited the UK in October and stayed there for a week. I didn't get this job.

Now I have a job interview in another company (company B),
This company will also sponsor flights, hotels and everything in between

When I applied for my visa, I mentioned the purpose of a job interview and shared the company A visa invitation letters.

Now I want to go back to the UK (for 3 days),

  1. Will I need to reapply for the visit visa, or can I use the existing visa (as it is multiple entry and valid for 2 additional months)
  2. Could the airport immigration officer have questions about why I am coming in while the job interview (for company A) is already finished?
  3. Can I tell them it's for another job interview?
  4. Would I need to carry invitation letters from company A and company B