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## dependency management: how to ensure long-term stability of business software with changes to frameworks / things that are not supported?

I work for the internal IT department of one of the largest companies in my country.

The infrastructure and software systems are strongly based on Oracle Database.
Most business processes and business logic are built using SQL and PL / SQL batch jobs, importing data into the database, transforming, consolidating, communicating through DB bindings, etc.
This system has been built gradually over the past 30 years. It is a very homogeneous system, which also has its advantages.

Recently, there has been an impetus to move towards different technologies, diversify and become less dependent on Oracle (cost is a factor: we are hosting several hundred Enterprise Edition databases and thousands of standard editions).

However, a question often arises:
The Oracle database has been quite stable and backward compatible: how do we guarantee the long-term stability (more than 10 years) of the system in a more heterogeneous environment?
Let's say we have components A, B, C, D that use a certain framework, hosted in a cloud somewhere.
What happens if the cloud provider stops supporting the framework? What if components B and C are no longer compatible due to a major change?

I still haven't heard a satisfactory answer, basically the only answer I got so far was "we'll just have to rewrite it"

So I hope to find out what strategies should be used to avoid basically having to rewrite everything every 3 years.

## pdes analysis – Stability and symmetries

In solitary wave stability theory, I have seen many times that people mention some of the symmetries of the equation to introduce the "correct" notion of stability. For example, if we consider the KdV equation $$u_t + u_ {xxx} + uu_x = 0, qquad (t, x) in mathbb {R} ^ 2,$$
this equation has solitary wave solutions $$u (t, x) = phi_c (x-ct)$$ and is invariant under space translations, that is, if $$u (t, x)$$ is a solution of the equation, then so is it $$u (t, x- gamma)$$ For any $$gamma in mathbb {R}$$. I have seen many times that the authors say that: since the equation is invariable in spatial translations, the correct notion of stability is "stability module of this symmetry". I understand that the correct notion of stability is "orbital stability" (otherwise we could disturb the velocity of the traveling wave and then it will be impossible to "stay close" to the evolution of the initial wave if we do not consider its orbit). However, I don't understand this specific sentence because, for example, you might ask, what about the other symmetries? Why do we never consider the "correct notion" of stability modulus all other symmetries in the equation? I am aware that KdV has infinity of them, so it seems a bit strange to me to establish this supposed relationship between orbital stability and the symmetries of the equation and forget about all the other symmetries at the same time.

Of course, this is not a peculiarity of the KdV equation, we could also consider, for example, the NLS cubic equation, which also has traveling wave solutions and infinitely many symmetries, however, the notion of orbital stability only considers some of them. . So I wonder if there is something I don't understand correctly. Does anyone have any explanation for this, I would really appreciate it.

Edit: Sorry, I just noticed that I never mention the notion of stability in the KdV equation. This notion corresponds exactly to always staying close to the "orbit" of the solitary wave, that is, staying close to the set $$Omega_c: = { phi_c (x-y): y in mathbb {R} }.$$

## Riemannian geometry – Stability of bubbles under heat flow

Leave $$Phi: S times (0, infty) a M$$ be Struwe's weak global solution to the heat equation with soft initial data $$phi: S a M$$, where $$S$$ it is a compact surface and $$M$$ it is a compact three-dimensional Riemannian manifold. Except at finite points in space-time, $$Phi$$ it's soft. At these singular points, non-constant harmonic maps $$S ^ 2 a M$$ "bubble" in the precise sense described by Struwe in 1985.

My question is about the stability of these bubbles under small disturbances from the initial data. Specifically, leave $$phi_k: S a M$$ be a sequence of maps such that $$phi_k to phi$$ at $$C ^ infty$$ rule. Suppose that $$Phi_k: S times (0, infty) a M$$ is a sequence of weak solutions with $$Phi_k ( cdot, 0) = phi_k ( cdot)$$ cast $$(x_k, t_k) in S times (0, T)$$ are singularities of the respective $$Phi_k$$ in which bubbles $$u_k: S a M$$ to form. Suppose also that the $$u_k$$ converge on $$C ^ infty$$ to a harmonic map $$u$$. Yes $$(x_k, t_k) to (x, T)$$It is true that $$Phi$$ has a bubble of $$u$$ to $$(x, T)$$?

## STABILITY – stabiluty.com

I am not the administrator or the project owner, I don't know!

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