equation solving – Finding analytic expression with replacement rules

I have a function defined as

f(k_):= Maximize({(x^2/(1+x^2))((1-x^(2k))/(1+x^(2k+1)))^2, 0 <= x <= 1}, x)

I would like to find an analytic form of $f$ as a function of $k$.

Differentiating the argument of the Maximize in $f$ with respect to $x$, I obtain the condition:

1+x^(3+4k) - x^(2k)(1+x)(x^2(1+2k)- x + (1+2k)) == 0

Is there a way I can write a replacement rule in Mathematica to substitute the above condition on $x$, and get $f$ as a function of $k$ alone?

Replacement in a While loop

I want substitute m for n in n = -3; While[True, If[2 n^2 + n - 6 == 0, Break[]]; n += 1/2];n

Here is what I want.

 m = -3; While[True, If[2 m^2 + m - 6 == 0, Break[]]; m += 1/2];m

I have tried this below.

{n = -3; While[True, If[2 n^2 + n - 6 == 0, Break[]]; n += 1/2]; n}/.n->m

Only get {m} in the output. it failed to get the result that I want.

Is there a modern replacement for a ComboBox?

ComboBoxes do a good job when on (e.g.) web forms.

However, they just look dated in a modern UI with a touch screen. Is there a more modern alternative to them? Or is it just a case of stripping away the ugly drop-arrow button?

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pattern matching – Replacement rules which for elements of a vector which meet conditions

I’m trying to create a function which will replace elements of a list with their values modulo 1, i.e. Mod[x,1], but only if Abs[x]>1. So, for example, the function would yield:


I’m trying to do this in an elegant way. For example, I have a function for a related purpose:

C1[v_] := v /. _?Negative -> 0;.

This replaces negative elements of a list with 0, and it’s very clean.

I’d like to do something similar. My efforts so far have included breaking it into two functions:

CLim[x_] := Mod[x, 1] /; Abs[x] > 1;

C2[v_] := CQubitLim /@ v;
But then, when I apply C2 to a list, it only seems to apply on some elements, for example


My other idea was to use a conditional rule


But this doesn’t seem to evaluate when I put a vector through it.

Any ideas much appreciated.

replacement – Replace the values of the second position in a list given two conditions

Suppose I have the following list:


and I have a given value of maxDh (let’s say 0.5) . How can I replace only the values in the second position with a given operation (e.g. dhMax*5) only when the values of the first position are greater than 74 and dhMax is lower than 1.2 (as in this case)?. For example given that in this example mxDH=0.5, then I would get: {{40,0.0712996},{40.,0.0712996},{40.,0.0712996}......{74.0202,2.5},{74.0404,2.5},{74.2023,2.5}....etc.

Thank you very much in advanced,

blockchain – Fee replacement issue – Bitcoin Stack Exchange

& # 39; Replace with rate & # 39; (RBF) is a method of increasing the fee rate for a transaction not yet confirmed. As a user, if you submit a transaction and then realize that the rate has been set to low, you can use RBF to create a replacement transaction that includes a higher rate, hoping for faster confirmation.

In this case, it appears that there was a transaction enabled with RBF that paid those funds to the 18dC... address mentioned in your screenshot. Otherwise, this transaction would be a normal bitcoin transaction, which has only the & # 39; RBF indicator & # 39; enabled. so that it can be replaced if the user so wishes.

If you didn't create this transaction, you should consider the fact that the machine your bitcoin wallet is running on is infected with some kind of malware. Without further information, it is not really possible to say with certainty what happened here.

replacement – Replacing an indexed term

Consider the expression:

s(i_, n_) := Sum((e(c(j)) + e(z(j)))*(l(i, j) + m(i, j)), {j, 1, n})

I’m trying to replace e(c(3)) by c(3) and have attempted

s(i, n) /. e(c(3)) -> c(3)
FullSimplify(s(i, n), c(3) == e(c(3)))
Eliminate({f == s(i, n), c(3) == e(c(3))}, e(c(3)))
Unevaluated(s(i, n)) /. e(c(3)) :>  c(3)
Unevaluated(s(i, n)) /. HoldPattern(e(c(3))) :> c(3)

But none produced the intended result. I think they all failed because the term e(c(3)) does not appear explicitly in the expression. How can we perform substitutions when that is the case?

terminal – Battery status and replacement

About a week ago my battery status (MBpro mid 17) claimed that the battery should be replaced after 250 cycles. Now, all of a sudden the battery status has returned to normal.

ioreg -l -w0 |grep Capacity

| |           "AppleRawCurrentCapacity" = 4921
| |           "AppleRawMaxCapacity" = 5067
| |           "MaxCapacity" = 5067
| |           "CurrentCapacity" = 4921
| |           "LegacyBatteryInfo" = {"Amperage"=0,"Flags"=5,"Capacity"=5067,"Current"=4921,"Voltage"=12751,"Cycle Count"=251}
| |           "DesignCapacity" = 6669
| |           "BatteryData" = {"StateOfCharge"=98,"PMUConfigured"=0,"Voltage"=12751,"QmaxCell1"=5827,"AdapterPower"=1100127202,"SystemPower"=3035,"ResScale"=200,"QmaxCell2"=6504,"QmaxCell0"=6376,"CycleCount"=251,"DesignCapacity"=6669}

Is it possible somehow to identify the problem with the battery that evoked the message to replace the battery?

certificate replacement

The following certificate on my iMac has expired and I cannot find a way to replace it.


Then what do I do? It seems to have to do with iTunes.