Relationship between focal length, perspective projection and camera distance

This page describes that the focal length does not cause perspective distortion. This page describes that an orthographic projection (which affects perspective) leads if you increase the focal length and the camera distance to infinity. So what is the mathematical relationship between focal length, camera distance and perspective projection?

P.S: If changing the focal length does not affect the perspective of the image, how does this affect the perspective distortion of the image?

linear algebra – relationship between a base and the number of vectors for polynomials.

I need to determine if the vectors below form a basis for the vector space of order 3 polynomials. The determinant of the matrix below is non-zero and it shows that all are linearly independent, but I read that for a dimensional vector space the number of vectors that form a base should also be n. In this case I have 4 vectors for a three-dimensional space. Does this mean that they cannot form a basis? I'm not entirely sure whether to assign dimensions to polynomials.

$$ (2-x ^ 2, x ^ 3-x, 2-3x ^ 2, 3-x ^ 3) $$

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Hello friends,

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Break a special repeat relationship


$ T (n) = T (n ^ { frac {1} {a}}) + 1 $ Where $ a, b = omega (1) $ and $ T (b) = 1 $

The way I solved it is as follows (using the method of changing variables as mentioned in CLRS):

To let $ n = 2 ^ k $

$ T (2 ^ k) = T (2 ^ { frac {k} {a}}) + 1 $

Put $ S (k) = T (2 ^ k) $ what gives $ S ( frac {k} {a}) = T (2 ^ { frac {k} {a}}) $

$ S (k) = S ( frac {k} {a}) + 1 $

Now let’s apply Master’s sentence,

$ S (k) = Theta (log_2 (k)) $

$ T (2 ^ k) = Theta (log_2 (k)) $

$ T (n) = Theta (log_2log_2 (n)) $

I think my method is wrong. Can someone help ?

Thank you very much

Taxonomy Terms – Categories REST API relationship to blog posts

I am new to Drupal.
I am trying to create a news app with Drupal as the backend.
I created a category taxonomy and linked it to the "Item" content type.
Then I created View for Articles Rest api and successfully get all the content. You can see here – link

Then I created a new rest API view for categories, which also returns the list of categories. shortcut

1. The problem is, how can I link the two? So I can return the list from
Posts in categories when the user clicks on a category name.

Second I would also like to display the list of categories and when someone clicks on a category all posts in that category should be returned.

This is a relationship problem. How can I achieve this? I am new to Drupal. Please help.

Python 3.x – What is the relationship and difference between the Process and Thread classes?

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Entity Framework Core build relationship one to many

public event {
public int Id {get; put; }
public string name {get; put; }

    public Categoria Categoria { get; set; }
    public CasaShow CasaShow { get; set; }
    public float QuantDeIngressos { get; set; }
    public DateTime Data { get; set; }
    public float ValorDoIngresso { get; set; }
    public DateTime Hora { get; set; }
    public bool Status { get; set; }

public sale {

    public int Id { get; set;}
    public IdentityUser  User { get; set; }

    public List Evento { get; set;}


Public class ApplicationDbContext: IdentityDbContext

   public ApplicationDbContext(DbContextOptions options)
        : base(options)
    public DbSet  Categorias { get; set; }
    public DbSet  CasasShows { get; set; }

    public DbSet  Eventos { get; set; }

    public DbSet  Vendas { get; set; }

    protected override void OnModelCreating (ModelBuilder builder) {
        base.OnModelCreating (builder);

        builder.Entity().HasMany(x => x.Evento);
        //Change my AspNetUser table to User
        builder.Entity ().ToTable ("User");

        //Change my AspNetRoles to Role
        builder.Entity ().ToTable ("Role");



I want a one-to-many relationship in which a sale receives multiple events, but the database does not recognize any of the declaration forms with ICollection, IList, List, or in the Builder With Many.

node.js – relationship between mongoose models

Guys, I have two models, one for creating events and the other for a user to register for the event. The problem is this: in the event creation model, I have a property that specifies the number of people who can go to my event, I have a route that, when the user clicks on it, passes their data on it, subtracts the number of people, who can go to the event. If I do this in my other model (event registration), does it subtract this can I do?

NOTE: I use Mongodb

How do I solve an equation for a given relationship?

This works for the example you posted. If you have another example where this doesn't work, try to fix it. This checks whether the combination of a x + b y can calculate to a common x+y Term, otherwise there is no solution.

solve(x_, y_, eq0_) := Module({lhs, rhs, eq, cx, cy, sol = {}, z},
   rhs = eq0 /. (lhs_ == rhs_) :> rhs;
   lhs = eq0 /. (lhs_ == rhs_) :> lhs;
   eq = rhs - lhs == 0;
   cx = Last@CoefficientList(rhs - lhs, x);
   cy = Last@CoefficientList(rhs - lhs, y);
   If(cx == cy,
    sol = (x + y) /. (First@Solve((eq /. (cx x + cy y) -> z), z) /. z -> ( x + y));
    sol = sol/cx
   x + y == sol

Now call it as

ClearAll(x, y, a);
eq = x + y == 3 + 2 x + 2 y + 38/a;
solve(x, y, eq)

Mathematica Graphics

eq = x + y == 3 + 4 x + 4 y + 38/a;
solve(x, y, eq)

Mathematica Graphics

eq = 2 x + y == 3 - 2 x - 3 y + 38/a;
solve(x, y, eq)

Mathematica Graphics

This does not return a solution because it cannot be collected x+y in one term

eq = 2 x + y == 3 - 2 x - 1 y + 38/a;
solve(x, y, eq)

Mathematica Graphics