analysis with a google sheet

I'm trying to get the number that is basically 116 in a cell in the google sheets with the following code, however, I'm missing the & # 39 ;; error before the declaration.

var copper = UrlFetchApp.fetch ("");

var copperObject = JSON.parse (copper);
Logger.log (copperObject.layers[‘copper’].getContentText ());

var fact3 = copperObject.layers[‘copper’].getContentText ());
var sheet3 = SpreadsheetApp.getActiveSheet ();
sheet3.getRange (2.5) .setValue ([fact3]);

Any help would be great!

Krypto 4 – Live trading, advanced data, market analysis, watch list, portfolio, subscriptions …

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Krypto 4 – Live trading, advanced data, market analysis, watch list, portfolio, subscriptions …

calculation and analysis: solve a restricted three-dimensional integration problem to obtain a "simplex magic" probability

Equation (7) in the 2012 document, "Complementarity reveals the entanglement of two twisted photons" by B. C. Hiesmayr and W. Löffler for a state $ rho_d $ In the "simplex magic" of the bell states.
begin {equation}
rho_d = frac {q_4 (1- delta (d-3)) sum_ {z = 2} ^ {d-2} left ( sum_ {i = 0} ^ {d-1}
P_ {i, z} right)} {d} + frac {q_2 sum _ {i = 1} ^ {d-1} P_ {i, 0}} {(d-1) (d + 1) } + frac {q_3 sum
_ {i = 0} ^ {d-1} P_ {i, 1}} {d} + frac { left (- frac {q_1} {d ^ 2-d-1} – frac {q_2} {d + 1} – (d-3)
q_4-q_3 + 1 right) text {IdentityMatrix} left[d^2right]} {d ^ 2} + frac {q_1
P_ {0,0}} {d ^ 2-d-1}
end {equation}

yields for certain values ​​of the $ q_i $& # 39; s, to $ d = 3 $ the Horodecki state of a single parameter, the first delimited entangled state found ".

More generally, for that matter $ d = 3 $, the restriction that requires partial transposition (obtained by transposing the nine $ 3 times 3 $ blocks) of the density matrix $ rho_3 $ being positive defined takes the form

restriction3 = q1> 0 && q2> 0 && q3> 0 && 4 q1 + 5 q2 + 20 q3 <20 && 512 q1 ^ 2 + 80 q1 (8-11 q2 + 4 q3) +25 (5 q2 ^ 2 + 16 q2 (2 + q3) +64 (-1 + q3) (1 + 2 q3)) <0

The command

To integrate[Boole[constraint3], {q1,0,5}, {q2,0,4}, {q3,0,1}]/ (10/3)

then, interestingly, it produces the "PPT probability" of Hilbert-Schmidt that the partial transposition of $ rho_3 $ it is positive defined,

(1/13720) (- 4312 + 5145 [Pi] + 2240 Sqrt[7] ArcCos[11/(8 Sqrt[2])]- 5160 Sqrt[7] ArcSin[(5Sqrt[(5Sqrt[(5Sqrt[(5Sqrt[7])/sixteen]- 6860 ArcTan[7] + 6280 Sqrt[7] ArcTan[(5Sqrt[(5Sqrt[(5Sqrt[(5Sqrt[7]) / 9])

which is approximately 0.461554. (This result was published as a comment in my previous query

Now, I would like to solve similarly the even more formidable $ d = 4 $ problem. Then, the restriction (found by the execution of the positive definition of the sixteen nested minors of both $ rho_4 $ and its partial transposition $ rho_4 ^ {PT} $) take the form

                restriction 4 = q1> 0 && q2> 0 && q3> 0 && q4> 0 && 5 q1 + 11 (q2 + 5 (q3 + q4)) <55 && 3375 q1 ^ 2 + 121 (7 q2 ^ 2 + 90 q2 (1 + q3-q4) +225 (1 +3 q3-q4) (-1 + q3 + q4)) <330 q1 (19 q2-15 (1 + q3-q4)) && (45 q1 + 11 (15 -7 q2-15 q3 + 45 q4)) (75 q1-11 (15 + q2-15 q3 + 45 q4)) <0

Execution of the order

To integrate[Boole[constraint4], {q3,0,1}, {q2,0,5}, {q1,0,11}, {q4,0,0,1}]/ (55/24)

would then give the corresponding probability of Hilbert-Schmidt PPT. (The GenericCylindricalDecomposition command suggested the particular ordering of the four variables for the 24 possible arrangements, but, of course, variations can be investigated).

Currently, using simply the free form of WolframCloud, my different attempts to perform the integration, by one method or another, are exhausted. In any case, the problem may be too formidable, by any means. (Maybe some transformations of variables could be effective).

Given these probabilities of PPT, the next question that would arise, of a nature that has never been addressed in a meaningful way, is how probabilities are divided between "entangled liaison" and "separable" states (see Fig. 3 of the appointment). Hiesmayr / Löffler paper).

This code can be used to generate $ rho_4 $

d = 4; W[k_, l_] : =
Sum[Exp[2 Pi I k n/d] Exterior[Times, S[n], S[Mod[n + l, 4]]]{n, 0,
d – 1}];
S[0] = {1, 0, 0, 0}; S[1] = {0, 1, 0, 0}; S[2] = {0, 0, 1, 0};
S[3] = {0, 0, 0, 1};
Omega[0, 0] = (1 / Sqrt[4]) Sum[
TensorProduct[S[s], S[s]], {s, 0, d – 1}]; Do[
Omega1[k, l] =
TensorProduct[W[k, l], Identity matrix[4] Omega[0, 0]], {16, 16}]/
Sqrt[4], {k, 0, d – 1}, {l, 0, d – 1}]; Do[
P[k, l] =
Exterior[Times, Omega1[k, l].ConjugateTranspose[Omega1[k, l]]], {k, 0,
d – 1}, {l, 0, d – 1}]; den =
Sum[c[k, l] P[k, l], {k, 0, d – 1}, {l, 0, d – 1}]rho[d_] : = (1 – q1 / (d ^ 2 – (d + 1)) – q2 / (d + 1) –
q3 – (d – 3) q4) IdentityMatrix[d^2]/ d ^ 2 +
q1 P[0, 0]/ (d ^ 2 – (d + 1)) +
q2 / ((d + 1) (d – 1)) Sum[P[i, 0], {i, 1, d – 1}]+ (q3 / d) Sum[
P[i, 1], {i, 0, d – 1}]+ (q4 / d) Sum[Sum[P[i,z], {i, 0, d-1}]{z, 2, d-2}]rho[4]

The partial transposition of $ rho_4 $ you get by

ArrayFlatten[Transpose[Divide[rho[Transpose[Partition[rho[Transponer[Dividir[rho[Transpose[Partition[rho[4], {4,4}]]];

Functional analysis. How can we make the derivative for this equation time t> 0

Leave $ x en[0,L]$ and consider the following equation,
$$ varepsilon left (t right) = frac {1} {2} int_ {0} ^ {L} {({{ rho} _ {1}} {{ left | {{vari} } _ {t}} right |} ^ {2}} + {{ rho} _ {2} {{ left | {{ varphi} _ {t}} right |} ^ {2}} + {{ rho} _ {1}} {{ left | {{ omega} _ {t}} right |} ^ {2}}} + b {{ left | {{ psi} _ { x}} right |} ^ {2}} + k {{ left | {{ varphi} _ {x}} + psi + lw right |} ^ {2}} + {{k} _ { 0}} {{ left | {{ omega} _ {x}} – l varphi right |} ^ {2}} + theta _ {1} ^ {2} + theta {2} ^ {2}) dx $$

where $ varphi $, $ psi $ Y $ omega $ they are functions whereas θ1 and θ2 are constants. Further, $ k_0 $,$ k $,$ b $ Y $ {{ rho} _ {1}}, {{ rho} _ {2}} $ with $ l = 1 / R $ are all positive constants where $ R $ is the radius of curvature

In this task we are interested in finding the derivative of $ varepsilon (t) $ w.r.t on time $ t> 0 $ .
First I think I use Leibtiz's rule to make this derivative that is presented in this Leibniz integral, this leads me to something wrong and it is not similar to the result I have in this document. Page 2

$$ frac {d varepsilon} {dt} = – {{ int_ {0} ^ {L} {({{ gamma} _ {1}} {{ left | {{left ({{ varphi} _ {x} + psi + l omega right)} _ {t}} right |} ^ {2}} + {{ gamma} _ {2}} {{ left | {{ psi} _ {xt}} right |} ^ {2}} + {{ gamma} _ {0}} {{ left | {{ omega} _ {xt}} – l {{ varphi} _ {t}} right |} ^ {2}} + left | {{ theta} _ {1}} _ {x} right |}} ^ {2}} + {{ left | {{ theta} 2x}} right |} ^ {2}}) dx $$
where everyone $ gamma $They are the viscosity coefficients. How did you derive it to obtain the previous result?

algorithm analysis – constant factor of a matrix

In Elements of programming interviews in Python by Aziz, Lee and Prakash, they say on page 41:

Insertion in a complete matrix can be handled by resizing, that is,
assign a new matrix with additional memory and copy over the
entries of the original matrix. This increases the worst case
insertion, but if the new matrix has, for example, a constant factor
larger than the original matrix, the average insertion time is
constant since the change in size is rare.

I capture the concept of amortization that seems to be implied here, but it seems to imply that in other cases, a newly assigned matrix could have a constant factor. less than the original matrix. Is that so? What does "constant factor" mean in this particular context? I'm having trouble understanding what is being said here. – Daily market analysis – News and analysis

Main trading ideas in the financial markets for 18.03.2019.

The main news creator of the previous week was the British pound. There was a strong increase in the cable against the main currencies in the Forex market. The British Parliament voted to discard a Brexit "without agreement" and requested to postpone the Brexit date beyond March 29.

That's why the weekly chart shows that last week produced a relatively large and strongly bullish candlestick, which reached a new high of 9 months, which is a bullish signal. It is assumed that this week will also be volatile because many British news is expected, including the decision on the interest rates of the Bank of England and the consumer price index. Therefore, we will be waiting at least 1.34 at the end of this week for the GBPUSD pair.

Price chart of GBPUSD - 03.13.2019

In addition to the Brexit vote, this week will likely be dominated by the launch of the FOMC and the contribution of the central bank of the Swiss National Bank and the Bank of England.

The EUR / USD rose close to 1.0% last week, recovering most of the losses suffered a week earlier. The key events of this week are the German economic sentiment ZEW and the German PMI and the eurozone. Investors will also be alert to the declaration of the Federal Reserve rate.
From a technical point of view, the EUR / USD showed a shooting star pattern and we believe that the market will probably fall back to the 1.1220 level before finding some buyers.

Price chart of the EURUSD - 03.13.2019

The Australian economy is showing signs of weakness, and analysts expect a rate cut of the RBA. If the RBA report indicated concern for political decision makers, the Australian could lose some points. In addition, the AUD / USD still shows a head and shoulders pattern on the 4-hour chart, which indicates a bearish outlook in the medium term. In that case, we are waiting for the AUDUSD pair on the 0.70 point

Price chart AUDUSD - 03.13.2019

From another point of view, in general, GDP data published by Statistics New Zealand can have a positive impact on ocean currencies. Then, experts have been waiting for a stronger release than the previous one.

Our objectives for:

GBPUSD – buying at 1.34
EURUSD – selling at 1.1220
AUDUSD – selling at 0.70 over a long term period


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Functional analysis. What is the difference between the methods to define a matrix function (canonical form of Jordan, Hermite interpolation and Cauchy integral)?

None: all are equivalent and all three return the same result for any function that is defined in the spectrum of $ A $. (Theorem 1.12 in Higham's book Matrix functions.) The only minor drawback of the Cauchy integral is that it needs the function to be analytic in a suitable region, including the eigenvalues ​​to make sense.

I'm not sure why you care about the definitions "in application"; they are only definitions, and this is not usually how they are calculated. If you are interested in its effectiveness as a method to actually calculate the matrix function, then that is another question. 🙂

How would you go about completing the Planning part, requirements modeling and analysis of the development process?

I am following the practice of RUP / USDP. I have created Use case model, High level, Use case, Expanded, Interaction diagrams and Class diagram.

Question: Explain how you would advance in this part of the development process.

Calculation and analysis – Replacement in integral.

So I have to make a substitution (u = pi / 2-x) in a definite integral, which I have defined as f[u], and when I place my code, no results are produced. The code that I have written is replace[Tointegrate[F[Integrate[F[Integrar[F[Integrate[f[u], X], {x, 0, Pi / 2}], u -> pi / 2-x]. Is there something missing in my code that I do not know?

My f[u]it is sin[x]) ^ n / (Cos[x]) ^ n + (sin[x]) ^ n) and I'm trying to replace u = u = pi / 2-x in it.

Thank you! – A mathematical beginner