## angular 8 fails going to lazy loaded modules directly after prod deploy

I have downloaded lazy-loading-ngmodules.zip from https://angular.io/guide/lazy-loading-ngmodules. I ran the app using ng serve with no problem. I can browse url http://localhost:4200 and click on Customers and Orders which both are lazy loading modules. I also can directly browse the url – http://localhost:4200/customers.

Then I built production version using ng build –prod and hosted it on IIS. I can browse the url http://localhost:80 and click on Customers and Orders to navigate to lazy loading modules. No problems!!! However, if I browse directly to the url http://localhost:80/customers, I got HTTP 404 Error. Why??? I need to directly browse to the lazy loading modules. How should I do it?

Thanks in advance!!!

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## Approximation of $\prod _{k=p+1}^{\infty } \cos \left(\frac{p \,\pi}{2 k}\right)$

After this post, I started wondering about possible approximations of the infinite product $$A_p=\prod _{k=p+1}^{\infty } \cos \left(\frac{p \,\pi}{2 k}\right)\tag 1$$ where $$p$$ is an integer. As far as I could see, there is no closed form expressions.

So, as I did in the linked question, I used Bhaskara I’s approximation (for $$-\frac \pi 2 \leq x\leq\frac \pi 2$$) $$\cos(x) \simeq\frac{\pi ^2-4x^2}{\pi ^2+x^2}\implies \cos\left(\frac{p\,\pi}{2k}\right)=\frac{4 \left(k^2-p^2\right)}{4 k^2+p^2}$$ and then computed $$B_p=\prod _{k=p+1}^{\infty }\frac{4 \left(k^2-p^2\right)}{4 k^2+p^2}=\frac{\Gamma \left( p+1-i\frac p 2\right)\,\, \Gamma \left( p+1+i\frac p 2\right)}{(2p)!}\tag 2$$ which does not seem to be very bad (see the table below).

Using Stirling approximation and Taylor series for supposed large values of $$p$$, I ended with $$\log(B_p)=\frac 12\log \left(\frac{5\pi}{4}\right)-\left(\log \left(\frac{16}{5}\right)+\cot ^{-1}(2)\right)p+\frac 12 \log(p)+\frac{11}{120 p}+O\left(\frac{1}{p^3}\right)\tag 3$$ What is interesting is to notice that $$\log \left(\frac{16}{5}\right)+\cot ^{-1}(2)\approx 1.62680$$ which is not so far from $$\frac \pi 2$$ ($$3.56$$% relative difference) and this already bring questions (at least, to me).

What is interesting is to see how close are the numbers in a logarithmic scale. $$\left( \begin{array}{cccc} p & (2) & (3) & (1) \ 1 & -0.85190 & -0.85120 & -0.84448 \ 2 & -2.17732 & -2.17725 & -2.16333 \ 3 & -3.61661 & -3.61660 & -3.59727 \ 4 & -5.10720 & -5.10719 & -5.08299 \ 5 & -6.62701 & -6.62700 & -6.59815 \ 6 & -8.16570 & -8.16570 & -8.13233 \ 7 & -9.71760 & -9.71760 & -9.67979 \ 8 & -11.2793 & -11.2793 & -11.2371 \ 9 & -12.8485 & -12.8485 & -12.8019 \ 10 & -14.4236 & -14.4236 & -14.3727 \ 20 & -30.3496 & -30.3496 & -30.2557 \ 30 & -46.4164 & -46.4164 & -46.2798 \ 40 & -62.5413 & -62.5413 & -62.3621 \ 50 & -78.6981 & -78.6981 & -78.4764 \end{array} \right)$$

Just out of curiosity, for $$1 \leq p \leq 50$$, I adjusted the parameters for the model $$\log(A_p)=a+b\,p+c\log(p)+\frac d p$$ and obtained a real good fit $$\begin{array}{clclclclc} \text{} & \text{Estimate} & \text{Standard Error} & \text{Confidence Interval} \ a & +0.69204 & 0.00006 & \{+0.69193,+0.69216\} \ b & -1.62255 & 0.00000 & \{-1.62256,-1.62255\} \ c & +0.50040 & 0.00003 & \{+0.50035,+0.50045\} \ d & +0.08598 & 0.00007 & \{+0.08583,+0.08613\} \ \end{array}$$ while is $$(3)$$, the coefficients are $$(+0.68394,-1.62680,+0.50000,+0.09167)$$ that is to say very very close.

For sure, all of this shows the high quality of the approximation of $$\cos(x)$$ but asks me questions about the value of $$A_p$$. If we truncate $$(3)$$ to $$O\left(\frac{1}{p}\right)$$,we should have $$A_p\sim \sqrt{\frac{5\pi p} 4 }\,e^{-\alpha \pi p}$$ with $$\alpha \approx \frac 12$$.

I wonder if we could find another better approximation of $$A_p$$ even at the price of more complex functions. Any idea would be welcome.

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## Erro ao rodar comando npm run prod

Estou com o seguinte erro ao rodar o comando “npm run prod” na máquina em produção que está na aws

node v11.13.0 npm v6.7.0

package.json Já apaguei o node_modules, o pakcage-lock.json e rodei novamente o “npm install” novamente

Os pacotes são instalados normalmente.

Porém retorna o erro a baixo quando executo o “npm run prod” Alguma luz?? rsrs

## How to save session data in prod server?

I want to save my data in a session: under drupal 8.6

I worked with “Private tempstore” it works locally but not in the server prod only if user is anonymous.

if ($this->currentUser->isAnonymous()) { session_start(); }  The same for the native php session. I ask if it can be stored with php configuration or how? thank you ## Disabling SSH access into prod vm on GCP As per title, for example if i disabled SSH access into vm on GCP. But if someone wants to remotely manage VMS , build docker containers and manage Cloud storage objects what they have to do? 1. Grant people access to use Google Cloudshell 2. Config VPN connection to GCP to allow SSH access to Cloud vms. My though: 1. If people asks for remote access to vm just like SSH, so if machine still has external id, they can access SSH using Cloud shell 2. Option 2 is possible if they mention external ip is removed but it seems like that is not the case. ## Notation: Using$\prod A_i$for noncommuting$A_i\$

I am writing up some math and realized that I do not know whether $$\prod_{i=1}^m A_i=A_mA_{m-1}\cdots A_1$$, OR whether $$\prod_{i=1}^m A_i=A_1A_2\cdots A_m$$.

Is there accepted consensus on this ordering?

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## Best Practices for managing Active Directory across Dev, QA, UAT, & Prod environments

Long time listener, first time caller. I’ve recently been promoted to my first Systems Analyst gig – and I’m very excited, if not a little green.

My organization just launched a a new in-house application that our Dev team has been working on for a few years, prior to my arrival.

Now that the application and integrations have been released to the production environment, the DevOps team is re-architecting the CI/CD pipeline, to be sure that each enviro is firewalled from each other. We have Dev, QA, UAT, and Prod environments.

The Developers are pushing hard for scripting everything, so that environments may be torn down and built up as needed. Of course, all the non-Prod environments need to mimic the Prod enviro as much as possible. Currently, Active Directory services are structured as a single forest, single domain.

Our shared concern is that – upon scripting the creation of the enviros, including AD elements (e.g. user accounts, service accounts, security and distribution groups) – we could inadvertently cause an undesired change to our single AD, which of course, is responsible for all production authentication (e.g. users, computers, etc…).

My question: What are some best practices for DevOps teams in terms of architecting/managing/isolating Active Directory across environments? Should we create another forest, with a trust relationship? Or maybe a child domain in the existing forest? Or something totally different?

If all the environments are uniquely their own – that is, firewalled and isolated from one another, but all reach out from within their isolation to have a “touchpoint” in a single AD, how is this best managed?

Looking forward to any guidance, and yes – I have been Google-fuing/researching independently of asking here. Just thought this community might be a good place to continue my search.

Please – if I haven’t provided the necessary information to appropriately answer the question, just let me know.

Thanks in advance.