Is there night in Alpha Complex?

I know that in principle as the GM I can run Alpha Complex any way I want. However, is there a canonical answer to whether or not Alpha Complex has a “night time?” There are plenty of quotes like “have a nice day-cycle” so there is a concept of one “day” (however long that might be). I don’t recall any source materials referring to light dimming or night-shifts or night clubs or the like.

Show that the complex series $\sum_{n=1}^\infty \frac{z^n}{n}$ converges for $z=i$.

I am trying to show that the complex series $ \sum_{n=1}^\infty \frac{z^n}{n}$ converges for $ z=i$ . I have worked out in a separate part of the problem that the radius of convergence is $ 1$ , but now I am trying to show it by substituting in $ i$ as follows:

$ \sum_{n=1}^{\infty}\frac{i^n}{n}=\frac{i}{1}-\frac{1}{2}-\frac{i}{3}+\frac{1}{4}+\frac{i}{5}-\frac{1}{6}-\frac{i}{7}+\frac{1}{8}+…$

$ =\left(-\frac{1}{2}+\frac{1}{4}-\frac{1}{6}+\frac{1}{8}+…\right)+i\left(1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+…\right)$

Here’s where I get stuck. I know that by splitting a summation into real and imaginary parts, if we can show that the real part converges and that the imaginary part converges, the complex series converges. So, assuming that nothing has gone wrong in my thinking up to this point, I need to somehow show that both of the above parts converge. How would I go about doing this, and what would the parts converge to?

The second derivative of a graph when finding point on inflections are complex. What do I do?

Letting second derivative equal to 0, I work out the points of inflection to be both complex. This confuses me a lot as it now wants me to find when it is increasing concavity and decreasing concavity. But I know that complex numbers are not ordered, so how would this be possible? It has a real stationary point, but then complex inflection points. Do I just… forget about the inflection points? Is it even an inflection point? I tried researching this and could not find anything about complex and derivatives.

Thank you!

Building complex sentences based on a data structure

I really do not like how bad this looks. It is not readable and I am not sure if I need the stacked map’s. There are a lot of iterations going on here (map, join, replace) and performance is really important, please help 🙁

Input:

const alternatives = [   "flex",   "float",   [     "background-size",     "background-image"   ] ] 

Expected Output:

'Consider using 'flex', 'float' or 'background-size' with 'background-image' instead.' 

Working Code:

const result = `Consider using $  {alternatives                  .map((alternative) => {                    return Array.isArray(alternative)                      ? alternative.map((a) => `'$  {a}'`).join(' with ')                      : `'$  {alternative}'`;                  })                  .join(', ')                  .replace(/, ([^,]*)$  /, ' or $  1')} instead.` 

How can create a simplified tool from this complex combination for data collection?

I am trying to create a tool on excel to collect data from different municipality to know their slum level. The values for the variables inside the first box (piped water…Bottled water) household data collected from surveys and are a percentage added up to form the Improved water(please have in mind that not all households/ area will have all the variables. e.g an area may have piped water but not public tap but a different area may have both. This will be the same for the improved sanitation, durable structure and sufficient living.

An area is considered a slum if it misses atleast one of the four main variables (improved water, improved sanitation, durable structure and sufficient living).

My calculation has been done on SPSS and thus the shelter deprevations figures. Basically, this table means that one shelter deprivation is a combination of all possible combinations with one variable missing. The same happens for two, three upto four where all are missing.

Finally all these combinations are brought together to get a non-slum area which is the value 44.5 in the yellow box. Taking from 100 we get 55.5% which is the slum percentage.

I am trying to see how best I can do the shelter deprivation part with excel to make a tool. The part in red shows what I got from multiplying the average (72.8) by the shelter deprivation values from spss. I got the value 54.10% as my slum which is not far off the real figure 55.5%.

Anyone know how I can tackle this. Below is the link with the image of my calculations

What technique(s) would you use to evaluate and [re]define fields in a lengthy and complex form?

We were commissioned the redesign of a web application for real estate agencies. During the first stage of our user research, which was a contextual inquiry, we found that the form fields (or data structure) for entering a new Property has many problems. There are fields that should not be mandatory, malformed fields, fields with incorrect options, maybe missing fields, etc.

We are looking for a user-research technique or method that allows us to evaluate the existing fields and determine the necessary changes in order to adapt the forms to current market practices and customer needs. The usual methods such as card sorting would not be very useful here, as it’s not a matter of labeling or sorting the fields.

Since we have seen differences of opinion between the real estate agents and some level of consensus must be achieved, I suspect we should use a quantitative technique rather than a qualitative one, but we are open to all possibilities.

Any ideas?

(Context: This is an application for the housing market in a latin american country with thousands of real estate agents, closed to the general public, which has been running for more than a decade with little to no UI or UX updates).

Confusion regarding CW complex structure of product

I find that if $ X,Y $ are CW complexes then $ X \times Y$ is a CW complex with skeleta $ (X \times Y)^{(n)}=\cup_{p+q=n} X^{(p)} \times Y^{(q)}$ .

So while considering $ S^n$ with CW complex structure:

$ X^0=*$

$ X^1=*$

…..

$ X^{n-1} = *$

$ X^{n} = S^n$

$ X^{n+1} = S^n$

….

What are the skeleta of $ S^5 \times S^7$ ?

By the above formula I have found it seems like,

$ (S^5\times S^7)^{0}=*$

$ (S^5\times S^7)^{1}=(S^5)^{(0)} \times (S^7)^{(1)} \cup (S^5)^{(1)} \times (S^7)^{(0)}=* \cup *$

$ (S^5\times S^7)^{2}=(S^5)^{(0)} \times (S^7)^{(2)} \cup (S^5)^{(1)} \times (S^7)^{(1)} \cup (S^5)^{(2)} \times (S^7)^{(0)}=* \cup * \cup *$

….

$ (S^5\times S^7)^{5}= S^5 \cup * \cup * \cup * \cup * \cup *$

and so on ?

My aim is not to find in particular the CW structure of this product but to clear the confusion regarding what is going on. Can someone please illustrate this example and help me understand!

Thanks in advance!

Complex channel based navigation modal

The application I am re-designing has a channel management modal for managing its customers. The admin hierarchy is as follows:

  1. My Company Admins
  2. Channel Admins
  3. Resellers Admins
  4. Customer Admins
  5. End Users

Each Admin can access and manage the account of the customer type below it and manage their own account through the same interface. Therefore Channels manage Resellers, Resellers manage Customers, Customers manage themselves and their users and End Users only manage themselves.

Each customer account has a customers list page, a number of settings pages and a user management list page. Each User within the user management list page has a number of settings pages.

The brand colour of the top bar and the logo change depending on what customer is being managed.

The idea is that My Company, Channels & Resellers switch between customer accounts using the search box at the top or via a list of customer under a customers section. Once a customer has been searched for and selected the brand in the top left corner changes to the brand of the customer being managed and all the navigation below the breadcrumb becomes the navigation for the customer being managed(Similar to how Facebook is navigated). The breadcrumb shows where the customer being managed is in the hierarchy and what page they are managing within the customer account.

Managing a customer enter image description here

Managing a customers user enter image description here

The feedback that has been generated so far is as follows:

  1. It is not intuitive to use the search to switch between customer accounts
  2. The three column structure for managing users takes up a lot of screen space
  3. Is the breadcrumb necessary as it takes up a lot of vertical space?
  4. It is not clear to click the first breadcrumb pin to get back to managing your own company
  5. The breadcrumb separates the top bar with the sidebar making the icon for collapsing the sidebar feel disconnected.

I am looking for guidance on how to better achieve this channel management navigation. Complete deviations from what I have here are welcome but if there is a way of salvaging this design modal that would be preferred.