## Bitcoin kernel: hash rate, transaction and block relation

I am aware that when the hash of the block header (block hash) is below the difficulty target, a block is considered validated.

But since I've never run a bitcoin node before (I'll do it soon), I had some questions regarding the mining process.

1) When the miners are running the BTC software, are they confirming by default the transactions in the memory group based on the higher tariffs, or are they authorized to choose which transactions they can validate?

2) If you have a higher hash rate, does this mean that you can also validate transactions faster?

3) When a block is validated on average every 10 minutes, as established by the BTC protocol, are the miners also trying to validate the transactions?

4) How are transactions validated?

## Study of the convergence of the integral single (relation: zero / zero)

I am looking for an examination of the convergence of the integral only:
$$int_0 ^ 2 frac { sqrt {2-x} , dx} {x ^ 2-5x + 6}$$

Any way to prove convergence without calculating the integral?

## mysql: application / database design where some records in a table have a relation of 1 to 1 with another table

I have an application where the requirements are to show a list of (just for example) car manufacturers. When you click on one of the manufacturers, a list of car models appears. You can then click on the car model to show other information. Each model has a lot of other data associated in several relationships from 1 to many (this is not important, but only to provide some background).

My problem is that one of the manufacturers must be treated as a car model. There will be only one car model under this manufacturer. The following is an example of the current database structure. As you can see, there is a manufacturer of MegaCar and there is only one model under this manufacturer. When you click on the MegaCar manufacturer, you must directly load the MegaCar model instead of displaying the model list.

``````+ ---------------
| manufacturers |
+ ---------------
| id | name |
+ ----- + --------- +
| 1 | Ford |
+ ----- + --------- +
| 2 | Toyota |
+ ----- + --------- +
| 3 | MegaCar |
+ ----- + --------- +

+ -------------------------------- +
| models |
+ -------------------------------- +
| id | manufacturer_id | name |
+ ---- + ----------------- + --------- +
| 1 | 1 | Focus |
+ ---- + ----------------- + --------- +
| 2 | 1 | Mustang |
+ ---- + ----------------- + --------- +
| 3 | 2 | Camry |
+ ---- + ----------------- + --------- +
| 4 | 2 | Corolla |
+ ---- + ----------------- + --------- +
| 5 | 3 | MegaCar |
+ ---- + ----------------- + --------- +
``````

I'm trying to decide on a database design and application design to represent this relationship. Basically, when someone clicks on the manufacturer's MegaCar, I'll need to load the model page for MegaCar (where models.id = 5), not the manufacturer's page (where Manufacturers.id = 3). I'll have to update the database schema for this. My current line of thinking is to add a `isModel` Flag to the manufacturers table and my code would look something like this:

``````object = getSelectedManufacturer ();
if (object.isModel) {
singleModel = query (& # 39;
SELECT MODELS.ID OF MODELS
INNER JOIN manufacturers ON models.manufacturers_id = manufacturers.id
WHERE manufacturers.id = [object.id]
LIMIT 1
& # 39;)
renderModelPage (singleModel)
}
else {
listOfModels = query (& # 39;
SELECT * FROM models
WHERE models.manufacturer_id = [object.id]
& # 39;)
renderManufacturerPage (listOfModels) // model list page
}
``````

The problem I have with this is that it can be confusing for other people who see my code. It also seems wrong that the relationship between these tables is one to many, but I'm making an exception for a record.

I had another idea to add a nullable. `modelId` column to the manufacturers table, but I did not like this for the same reason as the previous one. Also, I've seen some questions and answers here discouraging the use of NULL.

What would be the correct way to design this application?

## Fibonacci matrix for different constant values ​​in relation of recurrence.

For the fibonacci series we have a recurrence relation Fn = Fn-1 + Fn-2. Therefore, the initial matrix can be written as
eleven
1 0

where a[0][0]= Fn + 1, a[1][0] and a[0][1] they are Fn and a[1][1]= Fn-1
We can calculate nth Fibonacci by raising this matrix to the power of n.

What happens if the recurrence relation is Fn = Fn-1 + 4Fn-2? What will be the matrix?

I have a fibonacci recurrence relationship like the following:
Fn = 1 / sqrt (17) (((1 + sqrt (17)) / 2) ^ n) – ((1-sqrt (17)) / 2) ^ n))

## Analytical geometry: the cosine relation of the triangle in a complex plane.

I have a triangle $$ABC$$ In a complex plane. The arrangement of the vertices is counter-clockwise. The coordinates of $$A$$,$$B$$,$$C$$ are $$z_A$$,$$z_B$$,$$z_C$$ respectively.
You are given that side length. $$AB = c, AC = b$$ Y $$angle BAC = alpha$$. I need to find the other sides and angles of the triangle. How do I do this with complex numbers?

I know that with trigonometry using the rules of sine and cosine, you can derive the entire length and angles. But how to get it using complex numbers?

## Just be honest with them

The easiest way to get this resolved is if you are direct with them and tell them in advance what the first session will be. My experience has been that players are much more receptive to "script" events if they know they are coming, especially if they know that the world will open up a bit later.

Now, that does not mean I have to say what will happen, just that the first session is still setting the scene. You can still surprise them without keeping them completely in the dark. Just let them know in advance that certain events in the first session will be It happens, you can not change that, and that's all to configure for the rest of the campaign.

## Give them freedom in the way they follow their orders.

Even if the characters are receiving orders that they are expected to follow, that does not mean there is a specific way to follow those orders. By offering them different ways (or allowing them to do their own ways) to complete their tasks, it gives them enough freedom so that they probably do not feel pressured. If you can make your choices here affect events in later sessions, then probably your players will be very satisfied that they were able to shape the world in their first (scheduled) session.

I myself am a new DM and I only have a few sessions under my belt, but that is how I have approached the game so far. I discovered that my players are very forgiving when I am honest and direct with them, and they are much more likely to trust me when I obviously hide something from them. I can not guarantee that your players will act the same, but I can say that it worked with my group.

## To clarify what question I am answering:

Keep in mind that I am answering the question asked in the description and not in the title. As for what relationship between gameplay and cut scene should I know, I really can not tell you that. It really depends on what your players like and your style, although I would personally avoid using the material of the cut scene as much as I can.

## In relation to transit through Hong Kong – Travel Stack Exchange

You do not need a visa, as long as you stay in the airport's international transit area.

Timatic, the database used by airlines to verify passenger travel documents, establishes:

TWOV (Transit without Visa):
A visa is required, except for passengers with a confirmed confirmation.
Ticket (air-air or air-sea) to a third country within 48
They must remain in the international transit area and
Have the required documents for the next destination.

He did not ask, but regarding New Zealand, if you have a visa but there is no visa label in your passport, you must bring your visa approval letter.

Issuance of Visa:
New Zealand issues printed and unlabeled visa labels
visas The printed visa labels are inserted into a passport or
travel document. There is no physical evidence of a
visa without a sticker on the passport or travel document, but all
Passengers must carry a printed visa approval letter that
Confirm the details of your visa.

The New Zealand visa registration takes place in New Immigration
Zealand's systems and authority to address must be verified
using the NZ application system. Airlines not connected to NZ APP
that take a passenger at an earlier stage of their trip,
You can use TIETACNZ, or see the printed visa or visa label
approval letter to identify any travel condition, such as
if the person is exempt from the requirement to possess a
one way ticket

## Differential equations: resolution of the recursion relation of the coefficients of expansion of the asymptotic expansion of an ODE.

I want to solve the asymptotic solution of the following differential equation

$$left (and ^ 2 + 1 right) R & # 39; & # 39; (y) + y left (2-p left (b_ {0} sqrt {y ^ 2 + 1} right) ^ {- p} right) R & # 39; (y) -l (l + 1) R (y) = 0$$

as $$and rightarrow infty$$, where $$p> 0$$. I did the standard method obtaining a solution in series by prescribing the Frobenius method in the form

$$R (y) = sum_ {n = 0} ^ infty frac {a_ {n}} {y ^ {n + k}}$$
where $$k = l + 1$$ It is the indexical exponent. I had difficulty finding, by hand, a recurrence relationship for the coefficients. $$a_n$$ By arbitrary value of the parameter. $$p$$. At this moment, I'm just doing the brute force method to solve individual problems. $$a_n$$ for each value of $$p$$.

But I wonder if it is possible to get a recurring relationship using the Mathematica routine. Any help is appreciated.

## Differential equations – Recurrence relation for the asymptotic expansion of an ODE.

I want to solve the asymptotic solution of the following differential equation

$$left (and ^ 2 + 1 right) R & # 39; & # 39; (y) + y left (2-p left (b_ {0} sqrt {y ^ 2 + 1} right) ^ {- p} right) R & # 39; (y) -l (l + 1) R (y) = 0$$

as $$and rightarrow infty$$, where $$p> 0$$. I did the standard method obtaining a solution in series by prescribing the Frobenius method in the form

$$R (y) = sum_ {n = 0} ^ infty frac {a_ {n}} {y ^ {n + k}}$$
where $$k = l + 1$$ It is the indexical exponent. I had difficulty finding a recurrence relationship for the coefficients. $$a_n$$ By arbitrary value of the parameter. $$p$$. At this moment, I'm just doing the brute force method to solve individual problems. $$a_n$$ for each value of $$p$$. But I wonder if it is possible to solve the recurrence relationship. Any help is appreciated.

## beginner: sample size, P values ​​(their relation) and data visualization with graphics. ggplot and test t

We know that the P values ​​(within the context of the t test as an example …) are very sensitive to the size of the sample. A larger sample will produce a smaller p-value and everything else will be constant. On the other hand, the size of the Cohen effect d remains the same.

I am inspired by this code here, but I have changed some parts so that the difference between means is constant, instead of creating a random variable based on a normal distribution.

Although everything works, I imagine that some of the experts in this community could improve my syntax.

``````library (tidyverse)

ctrl_mean <- 8
ctrl_sd <- 1

treated_media <- 7.9
treated_sd <- 1.2

sample <- numeric () #crive vetor to group results
nsim <- 1000 #criar variavel
t_result <- numeric ()

for (i in 1: nsim) {
set.seed (123)
t_result[i] <- (media (ctrl_mean) -mean (treated_mean)) / sqrt ((ctrl_sd ^ 2 / (i)) + (Tratada_sd ^ 2 / (i))) #manual t test
sample[i] <- i # number of participants
}
ds <- data.frame(
sample = sample, #assign the sample size
t_result = round(t_result,3), #get the t test result
degrees = sample*2-2) #compute the degrees of freedom

ds %>%
filter (sample> 1)%>%
mutate (P_Value = 2 * pt (abs (t_result), df = degrees, lower.tail = FALSE))%>%
left_join (ds,.) -> ds

#plot
ggplot (ds, aes (x = sample, y = P_Value)) +
geom_line () +
note ("segment", x = 1, xend = sample, y = 0.05, yend = 0.05, color = "purple", line type = "dotted") +
note ("segment", x = 1, xend = sample, y = 0.01, yend = 0.01, color = "red", line type = "dotted") +
record ("text", x = c (1,1), y = c (.035, .001), label = c ("p <0.05", "p <0.01"))
``````