Show that $ (S ^ 1) ^ * = B ( ell ^ 2) $ knowing that $ ( ell ^ 1) ^ * = l ^ infty $

Is there a way to show that two trace class operators, $ S ^ 1 $, is $ B ( ell ^ 2) $, operators bounded on $ ell ^ 2 $, knowing that double $ ell ^ 1 $ is $ ell ^ infty $?

How to show that if R (unary relation) is primitive recursive (Stephen Cook exercise)

I study Recursive Functions and I found the online course notes of Professor Stephen Cook (the character of Cook's Theorem) link1, Link2.
In the notes, I found this exercise very interesting. I ask if there is a standard method to check if R (y) is a primitive recursive relation (R (y) is the set of any number equal to or less than x).

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Show how to get the big-oh for the following code:

void CountSort (int A (N), int range) {

// assume that 0 <= A (i) <range for any element A (i) int * pi = new int (range);

for (int i = 0; i <N; i ++) pi (A (i)) ++;

for (int j = 0; j <range; j ++)

for (int k = 1; k <= pi (j); k ++) cout << j << endl;


Could someone help me?

Why the plot does not show up?


Does anyone know why my plot does not show up? I receive a recursion error.

ω = Range(0, 5, 1);
U = 0;
μ = 0;
Σ(ω_) := 0;
G(ω_) := 0.5*(ω + μ - Σ(ω)) + 0.5*Sqrt((ω + μ - Σ(ω)) ^2 - 4);
G0(ω_) := ((G(ω))^(-1) + Σ(ω));
Gnew(ω_) := 0.5*G0(ω) + 0.5*( (G0(ω))^(-1) - U)^(-1);
Σ(ω_) := (G0(ω))^(-1) - (G(ω))^(-1);

Plot(Im(G(ω)), {ω, 0, 5})

algorithms – Show that the number of internal nodes in the PATRICIA tree is n-1 (for n elements)

I immerse myself in the data structures and the PATRICIA tree, in particular.
It is written almost in all resources that if the PAT tree is binary (for example, alphabet is {0, 1}), then there are n-1 internal nodes (where n is the number of elements), but the problem is that I can not find proof or find it on the web.
How can we show that the number of internal nodes is n-1 in this case?
Thank you!

Show html code on a website or wordpress site

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Should you submit a paper version of your e-visa when entering Myanmar with an e-visa or show it on a phone / tablet / laptop?

Electronic Visas for Myanmar:

You must bring this visa approval letter with you, as the Ministry of Labor, Immigration and Population asks you to produce it for verification upon your arrival in Myanmar.

Is it necessary to present a paper version of an electronic visa when entering Myanmar with an electronic visa, or to show the electronic visa on an accepted phone / tablet / laptop?

web development – How does the base URL of a website show the content of home.php?

The homepage of a website is served according to the configuration of the web server that hosts it.

By default, the default setting is as follows: When trying to reach the root of a directory, the server tries to serve a file named indexeither index.html, index.php or index.asp (usually the person who builds the website, software and infrastructure installed on the server or CMS used). The exact name of this file can usually be changed in the web server configuration.

If you had, for example, index.php and index.html in the same directory, the server configuration would decide again which one has priority and displayed.

If there is no file named index, an error is returned or a list of files and subdirectories of that directory is displayed (although this is considered obsolete behavior and many Web servers disable this feature by default because it can be serious – security risk, giving any visitor full access to the file structure is not a good idea).

A typical web server for a beginner (and even a much more advanced developer) would perform a LAMP configuration. This would first consist of an index.php file. If you set up a WordPress website on this server, you will find that it includes an index.php. The entire public side of the website would actually be directed to that file, with different content translated into instructions to allow it to load the different "pages" (actually, data stored in a database).

SQL Server – Data compression does not show up when writing index script on ssms

When I right click on SSMS and choose to create a script for the creation index:

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I receive this script, without the data_compression:

USE (APCore)

/****** Object:  Index (i_agencyId)    Script Date: 07/11/2019 12:18:13 ******/
    (agencyId) ASC
INCLUDE (   (countryCode)) WITH (PAD_INDEX = OFF, 

But when checking specific data compression with the help of the query below

use APCore

SELECT, p.data_compression_desc 
 FROM sys.partitions P
 INNER JOIN sys.indexes I ON I.object_id = P.object_id AND I.index_id = P.index_id
 WHERE P.data_compression > 0 and = 'i_agencyId';

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I receive the correct information.

I'm using this SSMS because I like my debug button:

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Is there a way to make ssms include data compression in the index definition when generating scripts?

My local host does not show the XAMPP localhost dashboard

I guess when you type http://localhost on your browser, this leads to a page called "WELCOME TO XAMPP" (if you are using xampp), which is localhost / dashboard. But for some reason, when I type http://localhost, that leads me to a page called "Index Of "