## general topology – When suspension and reduced suspension agree

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## graph – Grafana – general notification for whole dashboard

Is it possible to define general notificatin for whole dashboard in Grafana?
Let’s say we have many graphs on dashboard with defined thresholds. Is it possible to send general notification in case of any threshold has been crossed?

To make it clear:
Dashboard with graphs for severs of the same type. Each server has several licenses for some functionalities. Each license is depicted in separate graph. I don’t want to multiply notification definitions for each license. So it would be great if it would be possible to define notification once – which would point to the dashboard OR
define notification template and reuse in every graph.

regards,
Mike

## Find a general formula for \$int_0^{2pi}frac{sin^2left(frac{N+1}{2}xright)}{2pi(N+1)sin^2(x/2)} dx \$

My question is to solve
$$int_0^{2pi}frac{sin^2left(frac{N+1}{2}xright)}{2pi(N+1)sin^2(x/2)} dx$$

I know if we didn’t have the $$N+1$$ part and squares this integral should be $$1$$. Also upto $$50$$ or more Wolfram-Alpha solves this integral and gives $$1$$ for every integer. But i couldn’t prove this is the case for any $$Ninmathbb{N}$$.

## special functions – Is there a general unifying formula for the Laplace transform of a general weibull density?

It seems that the Laplace transform of weibull density has different formulas for rational shape parameters, depending on the degree of the numerator/denominator https://idp.springer.com/authorize/casa?redirect_uri=https://link.springer.com/content/pdf/10.1007/s11227-007-0150-4.pdf&casa_token=tRl3WDyIMqgAAAAA:bNeoMhSSxnQdOSQUAHx0aDVF_zVkwc6N4xaY3GhThfRLArXkqUhPkTWsfWHaq1-La1w1sy4CK7rMKnHW.

We can check this for various rational numbers.

``````Wb = WeibullDistribution[k, [Lambda]];
f = PDF[Wb, x];
L[s_] = LaplaceTransform[f, x, s,
Assumptions -> {[Lambda] > 0, k == 1/4}]
``````

If a general unifying formula exists, Mathematica does not know it

``````L[s_] = LaplaceTransform[f, x, s,
Assumptions -> {[Lambda] > 0, k>0, Element[k, Rationals]}]
``````

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## functions – Seeking for a general method to turn the term(s) in a formula into a list

If we want to make arbitary formula into a List, for example, input (1+a^3) and we want the output data to be {1,a^3}, we can use List@@(expr). However when input data becomes a^3, we need to change the code into List@(expr), otherwise we will get {a,3}.

But turning a formula into a list is just a internal process so I don’t know if the formula is of one term or a polynomial of many terms. I need a general method to turn any expanded formula into a list.

Thanks a lot for reading my question and sincerely hope you can offter a helping hand.

test data: 1.input (1+a^2*b^3), output {1,a^2*b^3}; 2. input (a^3), output {a^3}

## general topology – Giving the property of invertibility to zero using the Riemann sphere

From Tristan Needham’s Visual Complex Analysis, I learn that we can define $$frac{1}{0} =infty$$ by consider the rienman sphere / union-ing the $$mathbb {R^2}$$ with the point at infinity. But, doesn’t this lead to paradox:

$$0 cdot 1 = 0 cdot 2$$

Assuming invertibility of zero:
$$1 = 2$$

Clearly, this breaks some parts of multiplication and is clearly illogical, hence how is the newly defined inverse for zero consistent with the rienman sphere?

## mysql – General error 1114 when querying a table only 4% of the sotrage capacity in an RDS Instance

I have the followign problem when attemptign to draw stats on a table located in an Amazon AWS instance.

The table is composed of a huge list of names, dates and state two leter codes among other things. The dates are represented by a 6 digit code where the first four digits are the year and the last two digits the month (yes, we don’t care about the day).

I do a query to check the table size and it returns: 4097 MB which sounds about right.

But I also need to run the following query:

``````SELECT state_code,COUNT(date_code) as cnt,date_code FROM mytable WHERE (date_code > 200801) GROUP BY date_code,state_code  ORDER BY  state_code ASC
``````

Basically I want to know how many rows I have have for each date_code on each state.

My RDS instance is a db.m4.large running MySQL 8.0.23 with 1000 GiB of storage and a Maximum of 2000 GiB

I get this error:
Failed getting the number of obits by year and state. Reason: Select failure: SQLSTATE(HY000): General error: 1114 The table ‘/rdsdbdata/tmp/#sql7245_5bc3_1’ is full.

Now, there is a question very much like this one here: How to solve MySQL “The table is full” error 1114 with Amazon RDS?

However the solution is to simply increase the storage size, but 4 GB is only 4 % of the storage size. And this table will be ever increasing.

How could I solve this issue? Is the only answer to increase table size

Just FYI, this will be a very seldom query. Worst case scenrio something like once a day. I need for it to work, no really interested in making it fast. In case it matters.

## Looking for a general “blog health” check

Hi experts,

I’ve been blogging for over 15 years using a self-hosted WordPress plateform. I’m not really monetizing the blog, it’s mostly my portfolio and I focus on content creation.

Fifteen years is… ahem, a long time. Many things changed and I’m not exactly on top of latest dos and donts. The blog is fully functional but I’m sure it would benefits from a good cleanup and a fresh pair of eyes.

So I’m looking for someone to:

• Clean up old tables
• Perform a quick SEO check
• Fine tune plugin setup as needed (for instance, there’s apparently an issue with sitemap and the All in One SEO plugin… according to Google Analytics)
• Provide suggestions

This is the blog I’m talking about.

Interested? Let’ talk!