Zeros of an infinite series

To let $ sum_ {j = 1} ^ { infty} a_ {j} $ be a convergent series of positive numbers and $ {z_ {j} } _ {j = 1} ^ infty $ a closed discrete subset of the opened device disc $ mathbb {D} $, Then $ h (z): = sum_ {j = 1} ^ { infty} frac {a_ {j}} {z-z_ {j}} $ is a meromorphic function $ mathbb {D} $,

The question is: if we consider only the case of the infinite sum, then $ h (z) = sum_ {j = 1} ^ { infty} frac {a_ {j}} {z-z_ {j}} $ always an infinite number of zeros $ mathbb {D} $? Note that $ h $ never disappears outside $ mathbb {D} $,

This question comes from the following article (example 1.1 and question 3.3). Every comment is welcome.

https://arxiv.org/pdf/1709.03112.pdf

nt.number theory – Collection of equivalent forms of an exact statement: The number of elements of a precisely defined set is infinite

This main objective of this forum is to collect a "large list" of equivalent forms of mathematical (especially in number theory) problems that fit a statement of form:
The case (ON) is true if and only if The number of elements of a well-defined set is infinite,

The inclusion of appropriate references for each reformulation is urgently needed.

An example of such a situation is:

The Riemann hypothesis applies exactly when the number of Extremely abundant numbers is infinite.

This is proved in: Sadegh Nazardonyavi and Semyon Yakubovich, Extremely Lush Numbers and the Riemann Hypothesis, Journal of Integer Sequences, Vol. 2, no. 17 (2014), Article 14.2.8.

formal languages ​​- Can all Turing-computable problems be solved with a finite-tape machine and infinite controls?

Assuming that the tape is always long enough to hold the input, then with infinite control you can choose any language. The infinite control can only contain one state for each possible string that has been read so far. When it has reached the end of the input, it can accept or decline accordingly.

Nonlinear optimization – The proof of an infinite problem of norm minimization has finite support (non-convex p-norms)

Consider an optimization problem for infinite variables:

$$
begin {align}
min_ {x} ~ & { left lVert {x} right rVert} _p
\
text {s.t} ~ & left langle x, v_n right rangle ge 1 ~, ~ forall n = 1, dots, N
end {align}
$$

from where $ N in mathbb {N} $, $ x $ and $ left {v_n right } _ {n = 1} ^ {N} $ are all infinitely long vectors,
the $ v $& # 39; s are constant vectors and $ { left lVert { cdot} right rVert} _p $ is the $ p $-Standard.

I want to prove that there are optimal solutions $ x ^ * $ where the solution supports, d. H. $ text {supp} left (x ^ * right) $is finite (with the support of a vector being nonzero entries).

I am especially interested in cases where $ 0 <p <1 $, when the objective function is no longer convex,


When $ p = 1 $is there some known evidence (e.g. on May 2018), but as far as I understand, they all use convexity of $ p $-norm when $ p ge 1 $, e.g. Apply a strong duality to the dual problem and show that there are optimal solutions with maximum support $ N $,

I started to read about quasi-convex optimization (since then $ p $standard for $ p in left[0,1right]$ are almost convex), but I thought maybe there is a simple solution that I miss.


Any help or guidance is greatly appreciated.

html5 – Canvas Infinite Map: How to display objects with static X, Y, even if they are in a loop

I've created an HTML canvas example of an infinite scrolling map of objects in static locations. As you can see in the violin below, as you move to the left with the arrow keys, you can see that the card does not show the other end tiles and the objects are not displayed.

After changing the position on the opposite edge of the map, the tiles and the object are displayed from that side of the map.

I made this violin by modifying another violin, but it makes my point clear.
https://jsfiddle.net/n8d5kbau/

Is there a way to duplicate one edge of the map, or am I approaching the right path? I looked everywhere for it and finally decided to ask here.

Thank you in advance.

c ++ – Why does this function ask for name and number at the same time, and if you enter one, does it cause an infinite loop?

read pokemon (pokemon pok[TAM]short & d, short & num) {

Pokemon x;

cout << "Name of the Pokemon  n";
cin.ignore ();
getline (cin, x.name);

x.name[0]= toupper (x.name)[0]//; Put the first letter in capital letters
for (unsigned short i = 1; i <x.name.length (); i ++) // Run the string in full length
{
if (x.name)[i]! = & # 39; & # 39;
x.name[i]= tolower (x.name)[i]);
otherwise
(toupper (x.name)[i++]));
}


do
{
cout< "numero del pokemonn";
    cin >> x.num;
} while (x.num <0);

// We start the search for the Pokemon in the list of Pokemons
if (d == TAM) {
cout << "It is not possible to insert a Pokemon, since the list is full" << endl;
} else {
// We go through all Pokemons and look for it, if they are not found
// can be inserted and if the number of units is increased
short i;
for (i = 0; i <d; i ++) {
// If we find it, it can not be easily added
when (Pok[i].name == x.name || pok[i].num == x.num) {
cout << "The Pokemon you want to enter already exists, the number of units increases" << endl;
pok[i].units = pok[i]Units +1;
}
}


cout << "Enter Pokemon types separated by commas  n";
getline (cin, x.type);

do {
cout< "altura del pokemonn";
    cin >> x height;
} while (x.standard <0);


do
{
cout< "numero de unidadesn";
    cin >> x.units;
} while (x.units <0);


cin.ignore ();

// insert_order (pok, d, n);

return x;
}

}

Introduce bool (pokemon pok[TAM]short & d, short & num)
{
Pokemon x;

bool ok = true;
num = 0;

// pokemon x;
if (d <TAM)
{
// x = read ();
pok[d] = read (Pok, d, num);
insert_order (pok, d, num, x);
d = d + 1;
}
otherwise
{
ok = wrong;
}

for (short i = 0; i <= d; i ++)
num = num + pok[i].units;

Return ok;

}

How to convert an infinite decimal number from $ frac {23} {6} $ to a binary file?

How to turn a decimal number from $ frac {23} {6} $ in binary?

$ frac {23} {6} $ corresponds to $ 3.83333 bar {33} $where the numeral $ 3 $s are repeated forever.

I know how to translate finite decimal number in binary, but
Is there a way to translate such? Infinite decimal number to like $ frac {23} {6} $ in binary?

Every hint is appreciated!

mysql – Can a transitive join loop be infinite?

I have a table where an alternative product is stored:

+ -------------- + ------------- + ------ + ----- + ------- - + ---------------- +
| Field | Type | Zero | Key | Standard | Extra |
+ -------------- + ------------- + ------ + ----- + ------- - + ---------------- +
| alternate_id | bigint (20) | NO | PRI | NULL | auto_increment |
| company_id | varchar (36) | NO | MUL | NULL | |
| product1 | bigint (20) | NO | MUL | NULL | |
| product2 | bigint (20) | NO | MUL | NULL | |
+ -------------- + ------------- + ------ + ----- + ------- - + ---------------- +

I try to find products that are transitive, such as:

Enter the image description here

In the section above, I would like to query all products that are alternative to A (B, C, and D).

SELECT ... FROM table
- join some cool
WHERE product1 = A

Is that even possible with SQL?

How strong is a FSM with sufficient volume (but not infinite)?

Like Turingmachine, but your band is finally. To validate a program, it should have a borderline result if the tape length becomes infinite.

Whether the tape has two ends or is cyclic does not matter, because placing a specific point on a cyclic tape is like a two end tape and ends up running on a two-end tape that is cyclic.

It can also solve its own hold problem by testing the runtime. The conflict program is invalid, there is no result limit.

What is more?