vector analysis – Transformations of curvilinear coordinate systems

I’m reading a book covering multiple topics in mathematics and physics. There’s a chapter on tensors that had a very curious statement. It says “all curvilinear coordinate systems can relate to each other by some sort of rotation or series of rotations.” I don’t know what that precisely means. Does it mean that any curvilinear coordinate system can be transformed into any other one by rotations? It’s not obvious to me that that is indeed the case. And if so, can we formally show that this is in fact the case?
PS: The book is called Covariant Physics: From classical mechanics to general relativity and beyond.

operating systems – Can a java app that was bundled with modules of an x64 JDK (with jpackage), run on an x86 OS?

I am developing an app with a 64-bit JDK 16 on Windows 10. Since there is no JRE of this version, I am bundling the required modules with my app using Jpackage. Now my question: is this app going to work on 32-bit Windows? Do I need to install 32-bit JDK and compile my app with it in order to make it run on both 32-bit and 64-bit Windows systems? (I guess some of you might find it a silly question, so sorry for that).

Regards.

distributed systems – CORBA,MACH,JINI,TIB Rendezvous-: From where do I learn about these things?

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ds.dynamical systems – Does an “almost weak mixing” transformation admit a non null ergodic component?

Problem set up:

Let $mathbf X := (X, mathcal A, mu)$ be a standard probability space.

We say that a measure preserving transformation $T$ on $mathbf X$ is $varepsilon$-almost weak mixing if for every $delta > varepsilon$, and every pair of non-null measurable sets $A, B in mathcal A$, there exists an $N > 0$ such that for all $n > N$, we have $frac{1}{n} sum_{k = 1}^{n} |mu(T^{-k}A cap B) – mu(A)mu(B)| < delta mu(A)mu(B)$.

We say a measure preserving transformation $G$ on $X$ admits an ergodic component if there exists some non-null measurable subset $E$ of $X$ such that $G(E) subset E$, and the “restricted system” ($mathbf E, G_{|E})$, with $mathbf E := (E, mathcal A_{|E}, mu_{|E})$ is ergodic. Here $mathcal A_{|E}$ is the restricted sigma algebra, and $mu_{|E}$ is defined by $mu_{|E}(A) := mu(A cap E)/mu(E)$.

Question: Does there exist some $varepsilon > 0$ such that any $varepsilon$-almost weak mixing transformation $T$ on $mathbf X$ admits an ergodic component?

Remark: This is a potential sharpening of an earlier result.

For classifier systems, how is the genetic algorithm run on delayed class?

I am reading Signals and Boundaries and came across Classifier Systems. In the book, John Holland seems to imply that the signals in the input, as they come from a live environment, don’t have an immediate output known to the system (there is delay between the classification and the action). In every explanation I have seen online (e.g., https://en.wikipedia.org/wiki/Learning_classifier_system#Rule/classifier/population), it seems that it is expected that the input data comes in tag/class pairs, which makes it not true online learning. My question is: given that we do not know the class of a sample data tag in runtime, how is the fitness computed for the genetic algorithm step of the CS during online learning?

fa.functional analysis – Injectivity in the category of operator systems

An operator system $S$ is a self-adjoint subspace of a unital $C^*$-algebra $A$ such that $1in S$.

Let $mathscr{O}$ be the category of operator systems as objects and completely positive maps as morphisms. I want to prove that an object $I$ is injective in this category iff the condition $(*)$ is satisfied, where $(*)$ is the following condition:

If $Ssubseteq A$ is an operator system and $I$ is an operator system, then a completely positive map $S to I$ extends uniquely to a completely positive map $A to I$.

One direction is clear. For the other direction, it looks like I need to determine how the monomorphisms in $mathcal{O}$ look like. In particular , I think I can give a posive answer if monomorphisms in this category are unital or if the image of a monomorphism is again an operator system. Any help?

operating systems – How segmentation is solution to external fragmentation

As per Galvin book, Segmentation is the solution to external fragmentation. But in segmentation blocks are of different sizes. so if one segment is removed that creates a hole. if we put the small segment many times then this creates external fragmentation. then how segmentation be a solution to external fragmentaton?

replication – How Can I Find the Problems Occurred on MySQL-MariadbDB Systems?

I have built a three-node galera cluster, so it is a Master-Master replication structure. But sometimes the first node goes down and I can’t find the problem causing this. I am only looking at /var/log/syslog files. Where should I look to find the problems? Is there other log files I can look on production environment? Where the database admins looks for db errors?

operating systems – How could a page be invalid in demand paging?

I was reflecting on what I learned about demand paging and I have a question:
In demand paging, we have entries in the page table only for frames that are present in physical memory. So I was wondering how could a page fault (not because of a bug , occur in such a state).
In my class we where shown an image :
enter image description here

My confusion comes from the definition of demand paging. If every entry in the page table exists in physical memory then how could an invalid (not present in memory) entry exist in page table and cause a trap?
But then again, I thought to myself: Maybe when we need to replace a page and we exchange it with another one we do not replace the entry in the page table as well as we do with the frame but we change it’s valid bit to invalid and we add a new entry for the page that we just brought from disk. So basically, we these page replacements the page table of a process grows in time .
Is that right? Is that what happens? If so why we call it page replacement and not frame replacement?

macos – DLP + Employee monitoring on MAC systems

We are looking to implement Data Loss Prevention solution and employee monitoring in our system. In our network, we have many Macs which we want to secure. We want to protect ourselves from leaking data on a hard drive or on a cloud. We need to receive notification if someone tries to leak data, block it, and a way to check if the alert is real. Can anyone recommend a solution that he has experience with? We were recommended to use Teramind but it doesn’t work on MAC….