Ordinary differential equations: determination of the stability of the ode system

To consider $$ x & # 39; = a- (1 + b) x + x ^ 2y $$ $$ y & # 39; = bx-x ^ 2y $$

Find all the equilibrium points based on a, b. Linearize the system near the points and
Calculate the eigenvalues. Determine the conditions related to a, b with the stability of the instability of
balance points

What have I done:
The equilibrium points are given by $ f (a, b) = (0, b) $ Yes $ a = 0 $, $ f (a, b) = (a, b / a) $ Yes $ a neq 0. $ Then for the first point $ (x, y) = (0, b) $ that is to say $ a = 0 $, I found that the e values ​​are $ lambda_1 = – (1 + b) $, $ lambda_2 = 0 $So, what I am seeing is that for this point of equilibrium we have a stable line of equilibrium if $ b in (-1, infty) $I am not sure how to show if it is an asymptotic stability of Lyapunv's stability. Then for $ b in (- infty, -1) $ I have $ lambda_1> 0 $ which makes this unstable by this point. Next, I have that for the second point $ (x, y) = (a, b / a) $ that is when $ a neq 0 $, that $$ lambda _ { pm} = frac {- (a ^ 2- (b-1)) pm sqrt {(a ^ 2- (b-1)) ^ 2-4a ^ 2}} { 2} $$
that came from replacing this point of the equliprium in the Jacobian rule $ Df (x, y) $. I have trouble showing cases here. I will really appreciate any help.

dnd 5e: what are the main differences in style and system between D&D 5e and Pathfinder 2e?

D&D 5e has been optimized to be easy to learn and play, which is what you are reacting to. Its design reflects the fracture of the D&D fan base after 4e, and to a certain extent it encompasses a more "old school" style of play (read: 2e or earlier) in which the rules are much more nebulous, fluid and managed . ad hoc by the DM. This makes it easier to learn and play (since there are no rules to learn, you just have to rely on the judgment of the DM), and it also appeases some of the critics of 4e (and, to some extent, 3e) in a effort to gather the fan base.

The disadvantage of this is that most of the experience depends on the experience and criteria of the DM, and players often do not remain very confident in terms of how things will work from one DM to another. That makes it difficult to plan things as a player and, in some cases, can reduce the agency of players.

Pathfinder 1e was a D&D 3.5e spin-off, and for the most part it is identical in its fundamentals to that system.one D&D 3.5e probably never intended to be, but somehow it was a departure from 2e when it comes to the issue of "rules versus rules", since the most precise language gave many readers the basic assumption that things generally they would go mainly by the rules and that the exceptions would be, well, exceptional. Pathfinder inherited this inheritance, although Paizo tried to repudiate it, and despite the fact that, like 5e, Pathfinder was largely a reaction against D&D 4e, which was the system that really hugged the "rules" side of "rules versus rules".

With Pathfinder 2e, Paizo seems, at least somehow, to more fully embrace this ethos of "rules about rules", in a way that he largely did not do with Pathfinder. And, in ways that probably aren't coincidental, but I'm not sure they were planned, Pathfinder 2e really remembers D&D 4e. Class exploit lists feel very similar to the 4e power lists for each class, and the use of labels is very similar to 4e. Even the design and design of the book. it feels like 4e: the small action diamonds only resemble the intensive use of the character's 4e ♦ in the descriptions of power, and the nature of the diamonds of one or two or three is similar to the color coding of 4e for energy availability ( at will, meeting, daily)

Paizo has also discussed PF 2e in these terms, describing his audience as a person with a more technical mentality, more interested in the rules themselves, as interested in deepening them and combining them creatively. It seems that these appearances are not merely superficial, and possibly different to Pathfinder 1e, not involuntary.

In short, yes, it is quite likely that Pathfinder 2e at least intends to satisfy your tastes more than D&D 5e. You may also want to take a look at D&D 4e, which, as I mentioned, is likely to win "rules on rules" in general, even more than Pathfinder 2e.

  1. Pathfinder 1e Central Rule Book Y Bestiary they are based on, and in most things have the same rules as, 3.5e Player manual, Dungeon Master's GuideY Monster Manual. Pathfinder could not refer to the 3.5e supplements (since they were not open game content) and, of course, Pathfinder's own supplements after Central Rule Book They were never available in 3.5e.

domain name system – systemd-networkd: set DNS through CLI for the managed link

I want to configure the DNS for an interface managed by systemd-networkd through cli.
The file system is read-only, so is there a way to achieve this without manipulating any files?

I tried, for example:

systemd-resolve --interface eth0--set-dns 12.34.56.1 --set-domain lxd

This gives me the error:

The specified interface eth0 is managed by systemd-networkd. Operation refused.
Please configure DNS settings for systemd-networkd managed interfaces directly in their .network files.`

What I also tried is:

busctl call org.freedesktop.resolve1 /org/freedesktop/resolve1 org.freedesktop.resolve1.Manager SetLinkDNS 'ia(iay)' 2 1 2 4 8 8 8 8

What results in the error: Link eth0 is managed

I would like to manipulate DNS servers during runtime. No problem, when they are lost on restart.

Thanks in advance. πŸ™‚

dnd 5e – For seasoned / veteran players of DnD 5e and Pathfinder 2e. Could anyone simplify the "Big differences" in style, system, players?

D&D 5e has been optimized to be easy to learn and play, which is what you are reacting to. Its design reflects the fracture of the D&D fan base after 4e, and to a certain extent it encompasses a more "old school" style of play (read: 2e or earlier) in which the rules are much more nebulous, fluid and managed . ad hoc by the DM. This makes it easier to learn and play (since there are no rules to learn, you just have to rely on the judgment of the DM), and it also appeases some of the critics of 4e (and, to some extent, 3e) in a effort to gather the fan base.

The disadvantage of this is that most of the experience depends on the experience and criteria of the DM, and players often don't have much confidence in terms of how things will work from one DM to another. That makes it difficult to plan things as a player and, in some cases, can reduce the agency of players.

Pathfinder 1e was a D&D 3.5e spin-off, and for the most part it is identical in its fundamentals to that system.one D&D 3.5e probably never intended to be, but somehow it was a departure from 2e when it comes to the issue of "rules versus rules", since the most precise language gave many readers the basic assumption that things generally they would go mainly by the rules and that the exceptions would be, well, exceptional. Pathfinder inherited this inheritance, although Paizo tried to repudiate it, and despite the fact that, like 5e, Pathfinder was largely a reaction against D&D 4e, which was the system that really hugged the "rules" side of "rules versus rules".

With Pathfinder 2e, Paizo seems, at least somehow, to more fully embrace this ethos of "rules about rules", in a way that he largely did not do with Pathfinder. And, in ways that probably aren't coincidental, but I'm not sure they were planned, Pathfinder 2e really remembers D&D 4e. Class exploit lists feel very similar to the 4e power lists for each class, and the use of labels is very similar to 4e. Even the design and design of the book. it feels like 4e: the small action diamonds only resemble the intensive use of the character's 4e ♦ in the descriptions of power, and the nature of the diamonds of one or two or three is similar to the color coding of 4e for energy availability ( at will, meeting, daily)

Paizo has also discussed PF 2e in these terms, describing his audience as a person with a more technical mentality, more interested in the rules themselves, as interested in deepening them and combining them creatively. It seems that these appearances are not merely superficial, and possibly different to Pathfinder 1e, not involuntary.

In summary, yes, it is quite likely that Pathfinder 2e at least intends to satisfy your tastes more than D&D 5e.

  1. Pathfinder 1e Central Rule Book Y Bestiary they are based on, and in most things have the same rules as, 3.5e Player manual, Dungeon Master's GuideY Monster Manual. Pathfinder could not refer to the 3.5e supplements (since they were not open game content) and, of course, Pathfinder's own supplements after Central Rule Book They were never available in 3.5e.

hooks: module display enabled The following module is missing in the file system warning

I have a drupal 7 website where I want to install the optional email field module. The module will be enabled and will only work if I clear the cache. The hook_form_alter will be called and recognized and will work correctly. But after a few pages they update. This error will be displayed in the registration system.

User warning: The following module is missing from the file system

When I go to the module listing page, I see that the optional email module is still enabled, but none of the system hooks will be called and will work on the functioning website.

Error / var / lib / dpkg / lock: read-only file system

When I want to delete it, I get all this command, we are talking about what I am running from an HP THIN CLIETN T410.
rm: cannot be deleted <>: Read-oly file system

Why do conservatives oppose universal medical care so much when each country with that system pays less than the United States and gets better results?

By reading many of the comments below, about how big your insurance is, they often don't mention one thing, the existing insurance in the US. UU. It is still based on the ACA that Trump is still working to eliminate. The plan he supported would see increases for many in monthly premiums up to 500%, an increase in the amount of illnesses that insurers could refuse to provide coverage and a general reduction in the number of insured in the US. UU.

It is not ironic that when presented with the fact that the United States has one of the highest health care costs in the world and that countries that offer a form of universal Medicare pay less, they still deny reality. As someone mentioned Canada, I will use them as an example. A medical emergency in Canada, which requires an ambulance, paramedics and hospitalization costs the user about $ 160. A similar event in the USA. UU. It requires that the person be taken to the "right" hospital and, if not, it can cost up to $ 40,000. In Canada there are no "right or wrong" hospitals, just go to the nearest one. Yes, in Canada the government pays less per person than the US. UU. For better medical attention. While it is true that up to 40,000 Canadians seek medical assistance abroad, the rate for US citizens who go abroad, as a percentage of the population, is more than double that of Canada.

A study of the costs of medical care in the US UU. He discovered that a "medicare for all" type system would reduce costs for both the worker and his employer over time compared to the current system. This was done by a conservative inclined research group that generally opposed the principle of universal medical care.

Accept it, the United States is still working hard to have one of the worst health care systems in the world based on access and coverage for all its citizens. The last thing I knew was that it was the second worst, but the current administration is working hard to get that number 1 position.

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  • Contacts (CardDAV)
  • Calendar (to share, CalDAV)
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  • Rainloop: alternative webmail

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  • MailUser is the permission level with the ability to send and receive emails.
  • DomainAdmin manages all mail users in the domains that belong to them.
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Automatic migration allows you to migrate users and their emails without reset passwords, import them to the system manually or perform email data migration for each user

How does it work

  • Configure automatic migration for a domain with the details of your existing IMAP server (source)
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  • The system verifies your credentials with the source IMAP server, creates an account for them and migrates emails

Images

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cpu – What can we scale a system vertically infinitely?

Vertical scaling has limitations.

These limitations are called Physics and Engineering.

It turns out that Physics doesn't like doing too much work in one place, and our current engineering skills can only squeeze out so much useful work before it becomes useless noise.

Regarding the current performance:

  • You could go and look for the benchmarks for the various systems you are using.

  • You could go even further and compare a benchmark with a workload similar to the workload you have in mind.

Responses to your direct points:

  1. Stupid answer: in 2020, somewhere in the range of 64 GB to 1 TB based on specific hardware, it could be more, but that quickly becomes expensive.

    • Non-stupid answer: = Min(2 ^ bits in the pointer * number of system provided heaps, Max OS support Memory, Max supported Ram Module Size * Available Ram Slots)
  2. Stupid answer: in 2020 a few bytes of Tera.

    • Non-stupid answer: = Min(max file size in File system * Max number of files in file system * number of supported file systems, Max OS Support for File-system size, Number of available Drive Connection Ports * Max size of installable storage modules)
  3. Stupid answer: bits per second. Although you may be talking about the specific performance of the application, in which case concurrent connections or requests per second are better metrics.
    • Non-stupid answer: the slowest point of the network. It is probably the Internet link itself or the application that responds to network requests. Although it could easily be any of the network devices involved.