Operating systems memory management: help understanding a question related to segmentation

There is this question in my textbook (Operating Systems: Internals and Design Principles by William Stallings):

Write the binary translation of the logical address 0011000000110011
under the following hypothetical memory management schemes, and
explain your answer:

a. A paging system with a 512-address page size,
using a page table in which the frame number happens to be half of the
page number.

b.
A segmentation system with a 2K-address maximum segment size, using a segment
table in which bases happen to be regularly placed at real addresses:
segment# + 20 + offset + 4,096.

I am having trouble with understanding part b. I’m not a native English speaker. Initially, I assumed that “using a segment table in which bases happen to be regularly placed at real addresses” means that the segment number in the logical address is the number of the physical segment, but then I read this “segment# + 20 + offset + 4,096”, and I am not sure what to make of it. So does this mean that the base number in the segment table contains segment# (in the logical address) + 20 + offset (in the logical address) + 4,096?

woocommerce – Display related product categories by subcategory

I searched for relevant articles before but it could not be applied.

In Woocommerce, I just want to display products in subcategory, not show products in parent category, how to add code in file function.php, Child theme, don’t use Cross sell, up sell is available.

For example, the category tree is: Mobile> Apple> Iphone
The product is: Iphone 11
I only want Related products in “Iphone 11” products to show “Iphone” category, not show products in “Apple” and “Mobile” categories.

apache 2.4 – How do I further debug this Internal Server Error? (seems mod_fcgid related)

I was asked to help with a Drupal 7 site that I’ve helped to tweak several times before. The problem is, most of the site pages are not shown and “Internal Server Error” 500 page is shown instead (it started at the 6th of may). There are some exceptions though (these pages are loaded normally):

/user  (but not /user/1 for example)
/admin
/admin/content
/admin/structure
/admin/appearance
/admin/people
/admin/modules  (but not  /admin/config or /admin/reports)

(may be these are not all the exceptions, but I don’t know others yet)

Now, here’s what I know (I don’t have full root access, but I can request access for some resources):

  • PHPMyAdmin shows over 10K requests per minute (84% are select, 6% delete, 6% insert, ..). By the way, it also shows that it was started at the 7th of May (may be administrator has rebooted it)

  • httpd access_log consists of lines like (I splitted into 2 for readability)

    ::1 - - (13/May/2020:02:07:32 +0300) "OPTIONS * HTTP/1.0" 200 - "-"
     "Apache/2.4.6 (CentOS) OpenSSL/1.0.2k-fips mod_fcgid/2.3.9 PHP/5.4.16 (internal dummy connection)"
    

    there’s nothing except these ones (but I did some attempts to open the site during that period); these ones are added with frequency of about 5-20 lines per second

  • httpd error_log consists mostly of lines like

    (Wed May 13 09:16:09.487641 2020) (fcgid:warn) (pid 27860) mod_fcgid: process 25947 graceful kill fail, sending SIGKILL
    

    and these are added even less frequently: about 10 times per hour

  • the processor is highly loaded: it varies from 10% to 75% CPU consumed by /usr/bin/php-cgi php (which can be seen by using /usr/bin/php-cgi php; usage is increased when I try to load a page, I’ve seen it bumping from 10% to 50% in my manual tests)

Looks like something’s wrong with mod_fcgid, but I have very little idea of what I can do to debug and fix this. I also don’t understand why access_log doesn’t contain any entries regarding attempts to open pages (including successful ones). Can anybody help with this? How can I proceed with debugging?

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reference request – A terminology related to the definition of a mathematical structure

At the moment I am writing a textbook in Foundations of Mathematics for students and trying to give a precise definition of a mathematical structure, which is the principal notion of structuralist approach to mathematics, formed by Bourbaki. Intuitively (and on many examples) the notion of a mathematical structure is clear: this is a pair $(X,S)$ consisting of a set $X$, endowed with a structure $S$, which is a set somehow related to $X$. This relation of $S$ to $X$ is well-defined for first-order theories, which use the notion of a signature. What about the general case?

I arrived the the following definition and would like to ask some terminological questions.

The main idea is that a mathematical structure is determined by a pair $(sigma,mathcal A)$ consisting of a set $sigma$ called the signature and a list $mathcal A$ of $sigma$-axioms. By a $sigma$-axiom I understand a pair $(varphi,c_varphi)$ consisting of a formula $varphi$ whose free variables are in the list $x,s,g,c$, and a set $c_varphiin sigma^{<omega}=bigcup_{ninomega}sigma^n$.

So $c_varphi$ is some fixed tuple of elements of the signature $sigma$.
Therefore, a $sigma$-formula $(varphi,c_varphi)$ can be interpreted as a formula with free variables $x,s$ and some fixed parameters in the set $sigmacup{sigma}$.

Definition. A mathematical structure of type $(sigma,mathcal A)$ is any ordered pair of sets $langle X,Srangle$ such that for any $sigma$-axiom $(varphi,c_varphi)inmathcal A$, the formula $varphi(X,S,sigma,c_varphi)$ is satisfied.

The set $X$ is called the underlying set of the mathematical structure $langle X,Srangle$ and the set $S$ is called its structure.

In the list $mathcal A$ of $sigma$-axioms we can encode all desired properties of the structure $S$, for example that it is an indexed family $(S_i)_{iinsigma}$ and for some $iinsigma$ the set $S_i$ is a binary operation on $X$ satisfying such-and-such axioms, whereas for another $jinsigma$, $S_j$ is a relation on the power-set of $X$ (for example, satisfying the axioms of topology) etc, etc.

The question is how to call the pairs $(sigma,mathcal A)$ determining a type of a mathematical structure? Which properties of the list $mathcal A$ of $sigma$-axioms guarantee that mathematical structures of type $(sigma,mathcal A)$ form a category (for some natural notion of a morphism between mathematical stuctures of the same type $(sigma,mathcal A)$)?

I have a strong suspicion that such questions has been already studied (and some standard terminology has been elaborated), but cannot find (simple) answers browsing the Internet. I would appreciate any comments on these foundational questions.

Apps related to the icons on the upper left corner on an Android Samsung

enter image description here

Partial circle with inner circle arrow
and the rectangle with the clock_

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performance – How do I further debug this Internal Server Error problem? (mod_fcgid related)

I was asked to help with a Drupal 7 site that I’ve helped to tweak several times before. The problem is, most of the site pages are not shown and “Internal Server Error” 500 page is shown instead (it started at the 6th of may). There are some exceptions though:

/user  (but not /user/1 for example)
/admin
/admin/content
/admin/structure
/admin/appearance
/admin/people
/admin/modules  (but not  /admin/config or /admin/reports)

(may be these are not all the exceptions, but I don’t know others yet)

Now, here’s what I know (I don’t have full root access, but I can request access for some resources):

  • PHPMyAdmin shows over 10K requests per minute (84% are select, 6% delete, 6% insert, ..). By the way, it also shows that it was started at the 7th of May (may be administrator has rebooted it)

  • httpd access_log consists of lines like (I splitted into 2 for readability)

    ::1 - - (13/May/2020:02:07:32 +0300) "OPTIONS * HTTP/1.0" 200 - "-"
     "Apache/2.4.6 (CentOS) OpenSSL/1.0.2k-fips mod_fcgid/2.3.9 PHP/5.4.16 (internal dummy connection)"
    

    it seems there’s nothing except these ones; these ones are added with frequency of about 5-20 lines per second

  • httpd error_log consists mostly of lines like

    (Wed May 13 09:16:09.487641 2020) (fcgid:warn) (pid 27860) mod_fcgid: process 25947 graceful kill fail, sending SIGKILL
    

    and these are added even less frequently: about 10 times per hour

  • processor is highly loaded: it varies from 10% to 75% CPU consumed by /usr/bin/php-cgi php (which can be seen by using /usr/bin/php-cgi php)

Looks like something’s wrong with mod_fcgid, but I have very little idea of what I can do to debug and fix this. Can anybody help with this?

woocommerce – How to add related products outside “product-container”

So, I´ve been strugging trying to add related products outside the product container as I wanted them 100% width on my GP theme.

I´ve removed the related products through php & have added this code to make them display ONLY on product pages but hooked onto a full width section above the footer that´s readily availabe on GP.

/ADD-RELATED-PRODUCTS/
if ( is_product() ) {
add_action( ‘generate_before_footer’,’tu_function_name’ );
function tu_function_name() {
echo do_shortcode(“(related_products)”);
}}

Any idea why it only displays on 1 of the category pages and not on the product pages?

Second question is: By moving the related products into the body but outside of the product-container, would the related products go crazy or still show related products to that unique product page?

Thanks a lot!

rt.representation theory – A question related to newform and irreducible cuspidal representation og GLn

I was reading adelization of classical automorphic forms and learnt there each each cusp form correspond to a automorphic representation of $GL_n(A_mathbb{Q})$. I understood the proof. But then I found a statement like that there is a one-to-one correspondance between newforms of the congruence subgroup $Gamma_1(N)$ and the irreducible cuspidal representations of $GL_n(A_mathbb{Q})$.

But I couldn’t find any proof of it.
Please suggest some references.

Thank you.