can someone explain to me how research works?

I don't know the exact algorithms that are used, however, the basic idea for research is that every technology has a cost associated with it. Suppose Lasers costs 400 tp (not sure the real number). All the research facilities you build up creates a pool that is your max research units per turn. From your example above your max would be 40 tp per turn. This is the increased by any research bonuses you may have from racial abilities or research resources. However, you don't automatically use the full amount towards research each time. It is then modified by what percentage of your spending is allocated to reseach vs. military & social production. If you have your research set to 50%, then you can only apply up to 20 tp per turn. Finally, this is further modified by what percentage of your production spending you are using. If you have your spending set to 100% then you'd get to apply 20 tp per turn. If you had it set to 50% then it would only be set to 10 tp per turn. As I said above I'm not sure of the exact algorithms, and may have some of the ordering of the bonuses and costs incorrect, but this should cover the general idea.

Here is a WWW Link to the Wiki.
Maybe that will help you.

OK, this helps a bit.
Can someone tell me if this is correct?

Your research facilities set the "ceiling" for research points (flasks).

But you need money to reach that ceiling.

So, in my case, where one world has 40 tp, but I'm only getting 28 for my total empire, to get better research, I should invest in markets, not labs, right?

Here's the general idea:

You have two types of production you can spend your income on: research and manufacturing. Manufacturing is further divided into social (planet improvements) and military (shipbuilding).

The stated amount of manufacturing or research that a building produces is the amount that building will give you, provided you have the corresponding of the three sliders set to 100%, and the industrial capacity slider also set to 100%.

So to be clear, if you want to get that full 40 research from the one planet, you would set the three sliders to 0%/0%/100%, and industrial capacity (the one right below taxes) to 100%.

If at that point you're still earning a budget surplus, great. More money is always handy but it won't let you make any more research (unless of course you build more labs!). If you're running a deficit, well, you still get that full research amount, but you might not for long since at some point you'll run out of money!

The first two sliders determine how much of your manufacturing capacity gets used. If they add up to 100%, then you'll be getting all the mp that your factories are rated at, split between shipbuilding and improvements at the ratio you set the sliders at. Handily, if a particular planet is not building ships but not improvements, or vice-versa, and the one it does have work queued for has it's slider at at least 1%, the unused production will be funneled into the one that is needed. If nothing is being built at all on a planet, all the money spent on manufacturing there is refunded.

mainly true if it is to help you increase government spending. If government spending is already at 100% then it is much less true depending on strategy.

For example, i tend to use a strategy whereby i like to rush buy labs in my tech capital. I don't build anything else there, not even a starbase or a factory. In which case money is very important. However on other planets i am using for technology, it is not worthwile to rush buy labs, so in that case i will build at least 1 factory to help things along naturally, Money is less critical.