php – Best solution for thousands of requests

I have a project that needs to make more than 50 thousand POST requests with a proxy at the same time (without queues), several times a day, and treat the returned json data.

I currently use the App Engine platform of Google Cloud and I am developing the project in PHP.

What I have in mind:

  • Use PHP GuzzleHttp to send all requests at once and set the ‘concurrency’ to 50000 in Pool ();
  • Use Google Task to send personalized requests and return the answer to me to be treated in my App Engine service;
  • Use Parallel ( to handle everything in the App Engine service;
  • If it is necessary to use more than one instance, what would be the idea to divide these tasks?


  1. What would be the best technology in PHP?
  2. What would be the correct way to work this way on Google Cloud App Engine?
  3. What would be the configuration of the instances, ram, cpu etc?

can you help me? I will be very grateful!

Solution for the roots of $x^4+x^2+1=0$

Is this solution to find the roots of $x^4+x^2+1=0$ correct?






For this equation to be true, either $(x^2-x+1)=0$ or/and $(x^2+x+1)=0$.

Using the quadratic formula, I got




Are these values of x under the set of complex numbers the roots of $x^4+x^2+1=0$?

ap.analysis of pdes – classical solution of nondegenerate HJB equation

Let $bin C(mathbb R)$ and $L in C_b^2(mathbb R)$. Consider an equation
$$v_t (x, t) + inf_{ain A} {b(a) v_x(x, t) + a^2 } + v_{xx}(x, t) + L(x) = 0, hbox{ on } mathbb R times (0, 1)$$
with terminal condition
$$v(x, 1) = 0.$$
According to Theorem VI.4.2 of This Book, there exists unique solution $vin C_b^{2,1}$ if $A$ is compact. Does the same result still hold if $A$ is $mathbb R$?

contest math – I don’t understand how to reduce this fraction to the stated solution:

The fraction is as follows:

9 x 11 + 18 x 22 + 27 x 33 + 36 x 44 /
22 x 27 + 44 x 54 + 66 x 81 + 88 x 108

That’s all fine. What I don’t get is that my textbook says this reduces to the following:

9 x 11 + (1² + 2² + 3² + 4²) / 22 x 27 x (1² + 2² + 3² +4²)

I don’t understand how the sum of consecutive squares can be deduced from that fraction, or why the denominator contains “22 x 27 x “ as opposed to the numerator which is “9 x 11 +”

Any insight would be really appreciated!

summation – Closed for solution for $sum_{k = 0}^{n} Q^{k} ( 1 – Q) ^ {k}$

I know the binomial expansion formula:

(1 + x)^n = sum_{k = 0}^{n} {n choose k}x^k

However, I am trying to find (if there is any) a closed-form solution for the following equation.
sum_{k = 0}^{n} Q^{k} ( 1 – Q) ^ {k}

Could you guys point me to some solutions? TIA.

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javascript – Optimizing code solution for Palindrome Index-Hackerrank

I submitted my solution for palindrome Index coding challenge but I get “test cases terminated due to time out error”. My code is working and so I don’t know what else to do to optimize it. Please help:

function palindromeIndex(s) {
    let palindrome = s === s.split('').reverse().join('')
    if(!palindrome) {
        let i = 0
        let integerIndex = ()
        let arr = s.split('')
        while(i < s.length) {
            if(arr.join('') === arr.reverse().join('')) {
            arr = s.split('')
        return integerIndex.length > 0 ? integerIndex(0) : - 1
    }else {
        return -1

Solution to the same TXID from 3 different client

Someone sent me some bitcoins…. then I had some other clients sending me the same txid that they also made a payment, but I received only one payment.

numerics – Numerical solution to Integral equation by iteration

I want to solve the following integral equation
$$ rho(theta)=frac{rhoexp(-2L^2Dint_{0}^{pi} dtheta’sintheta’K(theta,theta’)rho(theta’))}{int_{0}^{pi} dtheta”exp(-2L^2Dint_{0}^{pi} dtheta’K(theta’,theta”)rho(theta’))} $$
$$ K(theta,theta’)=int_{0}^{2pi}dvarphi’sqrt{1-(costhetacostheta’ + sinthetasintheta’cos(varphi-varphi’))^2} $$
I thought I could start with a guess like $rho_0(theta)=(theta-frac{pi}{2})^2$: Inserting this guess in the previous equation I find a new $rho(theta)$, which I insert again in the equation, until
Is it possible to automate this process in Mathematica?

$L^2D$ is a parameter which can be, for example, equal to 5 or 10

calculus and analysis – Can you force Integrate[] to find a complete symbolic solution for all variables?

(As I’ve asked on the Math StackExchange and on a related previous question), I am interested in getting a complete symbolic solution to the integral of an expression with a lot of unassigned variables. If you combine some of the variables, the integral can be reduced to the form:

$$int_{-infty}^infty frac{text{A} Delta +text{B}}{left(Delta ^2+W^2right) left(text{C}+text{D}Delta +text{E}Delta ^2 right)}dDelta$$

Mathematica claims that the solution to this integral is:

$$frac{pi (text{B}-i text{A} W)}{W (text{C}-W (text{E} W+i text{D}))} text{if: } Imleft(frac{Epmsqrt{E^2-4 C E}}{E}right)<0 $$

Shown as code:

 (A1 Δ + B1)/((W^2 + Δ^2) (C1 + D1 Δ + E1 Δ^2)),
 {Δ, -∞, ∞}, Assumptions -> {W > 0})

Which returns:

ConditionalExpression((π (B1 - I A1 W))/(
 W (C1 - W (I D1 + E1 W))), 
 Im((D1 - Sqrt(D1^2 - 4 C1 E1))/E1) < 0 && 
  Im((D1 + Sqrt(D1^2 - 4 C1 E1))/E1) < 0 && Re(W) > 0)

Mathematica generates a conditional-expression, but doesn’t specify if this is a “full” answer. For instance what if we consider the integral under the domain of parameters with the opposite inequalities: $Imleft(frac{Epmsqrt{E^2-4 C E}}{E}right)>0$? Is there a solution in this domain of parameters?

I can try to force Mathematica to spit out an answer under different conditions. For example:

 (A1 Δ + B1)/((W^2 + Δ^2) (C1 + D1 Δ + E1 Δ^2)),
 {Δ, -∞, ∞}, 
 Assumptions -> {W > 0, Im((D1 - Sqrt(D1^2 - 4 C1 E1))/E1) > 0, 
   Im((D1 + Sqrt(D1^2 - 4 C1 E1))/E1) < 0})

I can get another symbolic answer for this new parameter space:

$$frac{i pi left(text{A1} D W+(-i) text{B1} sqrt{D^2-4 C E}-2 text{B1} E Wright)}{W sqrt{D^2-4 C E} left(C+W left(E W+i sqrt{D^2-4 C E}right)right)}$$

Is there an option to do this automatically and generate a solution for the entire set of possible combinations in the domain space? I’m honestly pretty surprised that it does not automatically return a combined piece-wise function with these different integrated results.

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