Maximum subsets of the odd index in $ mathrm {PSL} (3, q) $

To let $ G = mathrm {PSL} (3, q) $ to the $ q $ strange. I'm trying to understand a question that is about understanding the subgroups that contain a Sylow $ 2 $– Subgroups and especially subgroups with odd index in $ G $, I need to find a full description of the maximum subgroups of the odd index in the group $ G = mathrm {PSL} (3, q) $

PHP – Can an IF function be made for odd and even numbers?

They asked me to create an algorithm in PHP where the user enters 5 numbers and tells me whether they are even or not. I know how to do it, but I would have to create a formula for each one so that I could research and know that code storage functions can be created.However, TT didn't work for me and I've tried it a thousand times and nothing ,

Can someone help me? I only did it with 1 to save time because I did it with 5 and made mistakes.

NUMEROS PARES E IMPARES

Digite 1 numeros:=

;

and in the end I get

Note: Undefined variable: num1 in *****.

Please help me, I've tried the code in a thousand ways but nothing, I've seen videos but nothing, I know it's basic, but I don't see the truth where. Give me a tip or something to start with and I'll try C

Color a graph with an odd number of vertices with colors in linear time

We have an undirected simple connected graph with an odd number of vertices. We also know the number $ k $ This is actually the next odd number that is greater or equal $ Delta $, (So ​​if $ Delta $ is just, $ k = Delta + 1 $ otherwise $ k = Delta $.) i.e. $ k $ is the smallest odd number that is greater than or equal to the degrees of all vertices.

We want to find a linear time algorithm that is used to color the graph $ k $ Colours.

I am very new to graphing color algorithms. I know that a greedy algorithm is actually a linear time and can also color the graphics $ Delta + 1 $, But I cannot guarantee that I can dye with it $ k = Delta $ when $ Delta $ is odd.
Also, we should probably use whatever information the question gives us. an odd number of vertices is used somehow, but the greedy algorithm does not use this additional information.

How can I solve this?

Javascript – How do I subtract the even positions from the odd ones in a 2D array and assign a new array with the results?

I've been stuck in this problem for days. I have a multidimensional array whose first position is a Date () object. I previously reduced the arrangement by grouping each day.
I try to reduce each daily subarray with the results of subtracting the odd positions ("SALIDA") of the pairs ("ENTRADA").

Here are the dates:

const arrayHoras = (
  (
    "Thu Jan 02 2020 08:25:38 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Thu Jan 02 2020 13:30:43 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Thu Jan 02 2020 15:18:06 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Thu Jan 02 2020 18:12:22 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 08:35:38 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 10:15:23 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 10:59:16 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 12:25:01 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 12:31:33 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 13:20:43 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 15:28:06 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Fri Jan 03 2020 18:32:10 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Tue Jan 07 2020 08:31:46 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Tue Jan 07 2020 13:22:51 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Tue Jan 07 2020 15:30:00 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Tue Jan 07 2020 17:22:29 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Tue Jan 07 2020 17:31:59 GMT+0100 (CET)",
    "ENTRADA",
    "NOMBRE APELLIDO APELLIDO"
  ),
  (
    "Tue Jan 07 2020 18:32:30 GMT+0100 (CET)",
    "SALIDA",
    "NOMBRE APELLIDO APELLIDO"
  )
);

First step: We group the 2D arrangement by day of the first position of each element

const gruposDias = arrayHoras.reduce((acumulador, valorActual) => {
  const dia = new Date(valorActual(0)).getDate();
  if (!acumulador(dia)) {
    acumulador(dia) = ();
  }
  acumulador(dia).push(valorActual);
  return acumulador;
}, ());

const agrupadosPorDia = Object.keys(gruposDias).map(porDia => {
  return gruposDias(porDia);
});

Second step: I try to reduce the arrangements by day by subtracting the seconds between the data of the odd positions ("SALIDA") and those of the even positions ("ENTRADA"):

const entradas = ();
const salidas = ();
for (let i = 0; i < agrupadosPorDia.length; i += 1) {
  const agrupadosPorDiaI = agrupadosPorDia(i);
  for (let j = 0; j < agrupadosPorDiaI.length; j += 1) {
    if (j % 2) {
      const salidaTime = new Date(agrupadosPorDia(i)(j)(0)).getTime();
      salidas.push(salidaTime);
      rowSalida.push((ultRowConDatoSimulado += 2));
    } else {
      const entradaTime = new Date(agrupadosPorDia(i)(j)(0)).getTime();
      entradas.push(entradaTime);
    }
  }
}
console.log("entradas: ", entradas);
console.log("salidas: ", salidas);

My problem: With the second step, I lose the return of the "Entradas" and "Salidas" arrays within each subarray of the 2D array grouped by day.

Does anyone have the kindness to shed light on my decoder work?

If you misuse your knowledge, you can avoid the second step by expanding the array of the 2D array by expanding redu () and map (). I tried everything, I think.

Thank you in advance!!!.

linear algebra – let $ E, O $ subset $ F (R, R) $ be the set of even or odd functions. Prove that $ E $ and $ O $ are subspaces.

To let $ E, O $ $ subset $ $ F (R, R) $ denote the sets of even or odd functions. Prove that $ E $ and $ O $ are subspaces.

My proof: (For the sake of simplicity, I only show the proof of the set of even functions.

First we prove that there is a vector in 0 $ E $, To let $ a $ a straight function in $ E $ and $ x $ $ in $ $ R $, Since $ E $ is not empty, 0 exists $ in $ E with it $ a (-x) $= 0 = $ a (x) $, The same logic applies to the set odd function.

then we prove that the set of even functions is closed with the addition. To let $ x $ $ in $ $ R $. $ a $ and $ b $ then there are two separate straight functions $ (a + b) (- x) $= $ a (-x) $+$ b (-x) $= $ a (x) $+ $ b (x) $= $ (a + b) (x) $ $ in $ $ E $, Therefore, it is closed with the addition.

Next we prove that it is closed under scalar multiplication.
To let $ r $ $ in $ $ R $, then $ (r * a) (x) $= $ r * a (x) $= $ r * a (-x) $= $ – (r * a) (x) $ $ in $ $ E $Therefore, it is closed under scalar multiplication.

Therefore $ E $ is a subspace.

general topology – Infinite, Odd Möbius Strip

I've never dealt with topology or anything nearby, but I'm a curious outsider:

The standard Möbius strip is "rotated" once (is there probably a suitable terminology for this?); I am assuming that Möbius strips are created with an odd number of revolutions.

How would a Möbius strip work with infinite, if always odd, rotations compared to finite rotations?
Had it been assumed that the length of the material should not be extended, would the structure collapse to a point or to an infinitely thin line circle (would convergence / divergence come into play)?

Day 6: odd and even strings in C #

task
For an N-length string S indexed from 0 to N-1, the even and odd characters are printed as two spaces separated by spaces on a single line (see the following example for more information).

Note: 0 is considered an even index.

input format

The first line contains an integer T (the number of test cases).
Each line i of the T subsequent lines contains a string S.

limitations
1 <= T <= 10
2 <= length of S <= 10000

output format

For each string Sj (where 0 <= j <= T-1), output the even index characters of Sj followed by a space and the odd index characters of Sj.

Sample input

2
hacker
rank
example output

Hce akr
Rn ak
explanation

like so
static void Main(String() args) 

{

int t = int.Parse (Console.ReadLine ())

string () arrayOfStrings = new string (t);

for (int i = 0; i

{

string () = new string (i) (Console.ReadLine ());

}


formal languages ​​- basics of the PDA for strings with odd length and middle symbol 0

I don't understand the transition labels. In standard resources such as books by Ullman et al., Linz and Wikipedia, the transition names have the following form:

  • $ a, b / from $ means when the next input symbol is $ a $ and current stack top is $ b $and then press $ a $ on $ b $
  • $ a, b / epsilon $ means when the next input symbol is $ a $ and current stack top is $ b $, then pop $ b $
  • $ a, b / a $ means when the next input symbol is $ a $ and current stack top is $ b $, then pop $ b $ and push $ a $

I don't understand the meaning of transition labels in the diagram $ a, b rightarrow c $, Someone explained to me that it is the next input symbol $ a $pop $ b $ and push $ c $, I think if this interpretation is correct, this notation is insufficient because it describes both $ a, b / from $ and $ a, c / ac $ how $ a, epsilon rightarrow a $, Am I right or did I misunderstand the notation?