Show that the norms lp with 1 <= p, q <= infinite are equivalent

I want to show that for all 1 <= p, q <= infinite, there exists a, b such that a || x || p <= || x || q <= b || x || p for all x in X. Is there a way to do this without Hölder's Inequalities?

magento2 – Magento 2.3 – Urls from the storefront and the admin on localhost: 8081 show 404 / not found

I have a pretty similar problem, just on a Windows machine. Here is another step that you can try to see if it helps. So go to the pub / static folder and delete everything except htaccess. Then open app / etc / di.xml, look for the path "Magento Framework App View Asset MaterializationStrategy Symlink" and replace it with "Magento Framework App View Asset MaterializationStrategy Copy". Then empty the cache and maybe restart Apache and try again?
I come from http://www.dckap.com/blog/magento-2-admin-links-not-working-in-windows/ which is specific to Windows, but I do not think this problem is specific to Windows.

calculation and analysis – does Mathematica show that the differentiation of the integral of a function is not itself?

The calculation tells us that the differentiation of the integral of a function should be itself, but at least in one case, Mathematica answers NO. I feel very confused. The new figure seems to fork to a real root down.

The story is that I'm trying to integrate a function that includes an elliptical Jacobi function, and then something strange happens. When I traced the figure of the integral, I found that the sign of the slope does not correspond to the sign of the integral, that is to say to the original function. I can not understand what's wrong with Mathematica or there's something tricky about elliptical functions and elliptical integrals? The original function and its integral with the help of Mathematica software are presented as follows:

$$ text {mini} (m) = x_1 + frac {x_2-x_1} {1- frac {x_2-x_4} {x_1-x_4} text {sn} ^ 2 left[frac{m-m_b}{xi},kright]}. $$
or $ xi = frac {4} {i sqrt { left (x_2-x_3 right)} left (x_1-x_4 right)}} $ and Jacobi's module $ m = k ^ 2 = frac { left (x_1-x_3 right) left (x_2-x_4 right)} { left (x_2-x_3 right) left (x_1-x_4 right)} $, or $ x_1 = -2.73205 $, $ x_2 = 0.732051 $, $ x_3 = 1 – i $ and $ x_4 = 1 + i $. The constant $ m_b $ can be calculated as $ m_b = xi F left[i arcsinleft(sqrt{frac{(0.5 – x_2)(x_1 – x_4)}{(0.5 – x_1)(x_2 – x_4)}}right),kright]= $ 0.988254.

<img src = "https://i.stack.imgur.com/JRk1C.jpg" alt = "Figure for the mini (m) function with $ -10 <m<10$.">

$$ int text {mini} (m) text {d} m = x_1 m – frac { xi left (x_1-x_2 right) Pi left[n,frac{m-m_b}{xi},kright] text {dn} left[frac{m-m_b}{xi},kright]} { sqrt {1-k ^ 2 text {sn} ^ 2 left[frac{m-m_b}{xi},kright]}}. $$
or $ n = frac {x_2-x_4} {x_1-x_4} $.

<img src = "https://i.stack.imgur.com/dnaEB.jpg" alt = "Figure of the integral of the function mini (m) with $ -10 <m<10$.">

After calculating the numerical differentiation and plotting the figure with Mathematica, the figure below does not correspond to the original function mini (x).

<img src = "https://i.stack.imgur.com/J8Kwp.jpg" alt = "Figure for the differentiation of the integral of the function mini (m) with $ -10 <m<10$.">

For reference, my Mathematica code is:

mini[m_] : = (x1 x2 - x2 x4 - x1 x2 JacobiSN[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]^ 2 + x1 x4 JacobiSN[
1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]^ 2) / ((- x2 + x4) (- (x1 / (x2 - x4)) + x4 / (x2 - x4) + JacobiSN[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]^ 2))
intmini[m_] : = Integrate[mini[m], m]intmini[m]
x1 = root[#1^4 - 4*#1^2/1 + 8*#1/1 - 8*0.5 &, 1]
x2 = root[#1^4 - 4*#1^2/1 + 8*#1/1 - 8*0.5 &, 2]
x3 = root[#1^4 - 4*#1^2/1 + 8*#1/1 - 8*0.5 &, 3]
x4 = root[#1^4 - 4*#1^2/1 + 8*#1/1 - 8*0.5 &, 4]
mb = - ((4 I EllipticF[I*ArcSinh[Sqrt[-(((0.5 - x2)*(x1 - x4))/((0.5 - x1)*(x2 - x4)))]], ((x1 - x3) * (x2 - x4)) / ((x2 - x3) * (x1 - x4))]) / Sqrt[(x2 - x3)*(x1 - x4)])
Ground[Re[Re[Ré[Re[mini[m]], {m, -10, 10}]Ground[(M-mb)x1+(4I(x1-x2)EllipticPi[(X2-x4)/(x1-x4)JacobiAmplitude[(M-mb)x1+(4I(x1-x2)EllipticPi[(X2-x4)/(x1-x4)JacobiAmplitude[(m-mb)x1+(4I(x1-x2)EllipticPi[(x2-x4)/(x1-x4)JacobiAmplitude[(m-mb)x1+(4I(x1-x2)EllipticPi[(x2-x4)/(x1-x4)JacobiAmplitude[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]JacobiDN[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]) / (Sqrt[(x2 - x3) (x1 - x4)] sqrt[1+((x1-x3)(x2-x4)JacobiSN[1+((x1-x3)(x2-x4)JacobiSN[1+((x1-x3)(x2-x4)JacobiSN[1+((x1-x3)(x2-x4)JacobiSN[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]^ 2) / ((- x2 + x3) (x1 - x4))]), {m, -10, 10}

Needs["NumericalCalculus`"]
Ground[Re[DAKOTADUNORD[(M-mb)x1+(4I(x1-x2)EllipticPi[(X2-x4)/(x1-x4)JacobiAmplitude[Re[ND[(M-mb)x1+(4I(x1-x2)EllipticPi[(X2-x4)/(x1-x4)JacobiAmplitude[Ré[DAKOTADUNORD[(m-mb)x1+(4I(x1-x2)EllipticPi[(x2-x4)/(x1-x4)JacobiAmplitude[Re[ND[(m-mb)x1+(4I(x1-x2)EllipticPi[(x2-x4)/(x1-x4)JacobiAmplitude[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]JacobiDN[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]) / (Sqrt[(x2 - x3) (x1 - x4)] sqrt[1+((x1-x3)(x2-x4)JacobiSN[1+((x1-x3)(x2-x4)JacobiSN[1+((x1-x3)(x2-x4)JacobiSN[1+((x1-x3)(x2-x4)JacobiSN[1/4 I (m - mb) Sqrt[(x2 - x3) (x1 - x4)], ((x1 - x3) (x2 - x4)) / ((x2 - x3) (x1 - x4))]^ 2) / ((- x2 + x3) (x1 - x4))]), m, p]], {p, -10, 10}

The first graph relates to the figure of the original function, that is to say the integrand. The second plot is for the figure of its integral. The third is for the figure of the differentiation of the integral. The third digit should be identical to the first, but it is different. The sign of the third figure corresponds to that of the second figure of the integral. This seems to tell us that Mathematica gives an erroneous integral for the function, including elliptic functions, as the original function I used. I do not know how to calculate a correct integral of my original function. Welcome to all useful suggestions and help in Math and Mathematica!

PS: I would like to add an extra comment. In my case, the elliptic module m and the Jacobi amplitude are complex numbers and not real numbers. I wonder if there is a general theory of elliptic functions and elliptic integrals beyond the real elliptic module and the real Jacobi amplitude?

Software that creates a slide show film side by side?

I have a mixed media record (still images in jpeg format, of live motion heic, short MOV clips) of children in a class that builds a project. (Many hot glue guns!)

And I need to create an MP4 video slideshow of content to play on an HDTV screen. What I did using Apple Photos Slideshow, which allows me to quickly switch from a multimedia file to

But you have to take a closer look – each parent wants to see their own kids build stuff, and does not care about the other 23 / 24th media. Most of the photos are in portrait, so two portrait photos can be side by side.

Can the usual tools (ffmpeg, avidemux, etc.) be used to script such a beast? Tools that do that? I do not want to invest days in a video that will be viewed once.

Theme 2017 – the header image does not show on the mobile

I use the default WP Twenty Seventeen theme and have a header image enabled. When I select mobile in the customizer, the header image is displayed, but when I browse the site, regardless of the mobile device used, the image is not displayed.

No suggestion?

boot – acer uefi does not show the Windows hard drive

Acer TC-280-UR11 was running Windows 10 OK, just slowly. I had partitioned the 2 TB disk into two parts, so my disk "D" had my data. I've tried to migrate to an SSD using Acronis for Crucial. After the seemingly successful migration, neither the hard disk nor the SSD hard drive boot – BSOD "Your PC / device needs to be repaired or a required device is missing" error 0xc0000225. I restored the backup of my Paragon hard drive and got a similar error – 0xc000000e. I have tried a new installation from a Windows 10 1809 recovery media. It failed the first reboot – black screen "Restart and select the appropriate boot device or insert the bootable media into the device selected and press a key ". Same failure during a clean install from the Windows 8.1 DVD. Same errors under Windows 10 and Windows 8.1 when installing clean on the SSD drive. (I guess the black screen errors come from the BIOS, where does the BSOD come from?). I've installed Ubuntu as a dual boot system alongside the Paragon restore and everything works. I can run Ubuntu OR I can start and run all my old Windows 10 applications. I have re-flashed the BIOS. No change. It appears that the BIOS does not recognize a UEFI / GPT hard drive or SSD as long as the Windows Boot Manager is listed in the boot device list. I can boot from a UEFI USB drive, a DVD or hard drive if it is equipped with Ubuntu, but not from a Windows hard drive or from an SSD drive. I've also tried Ubuntu startup repair, EasyRE, all Internet startup error fixes such as rebuildbcd, fixboot, etc. Sorry for the long question, but I did my best to solve this problem myself. Is it the ACER BIOS (or is it Memorex? – I'm going out with myself). HELP ME!

show / hide the particular cell column when the mouse hovers over the grid line ag


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Algebraic topology – Direct search of a homotopy to show that two homomorphisms induced on a fundamental group are identical

Consider the following problem:

"Let $ I in pi_1 (S ^ 1, (1,0)) $ be the class of the identity card. CA watch $ nI $ is the class of the map $ f_n: S ^ 1 rightarrow S ^ 1 $ given by $ f_n (z) = z ^ n $.

I can solve it using the fact that $ pi_1 (S ^ 1) = mathbb Z $. But without assuming that, how can this problem be solved? I tried to build homotopic writing paths in the polar coordinates but I found none.

The WP Users Page does not show the number of users per role

I use a website that has 70,000 users imported from an old vbulletin forum. Everything works fine except a problem that I have on the users page in the backend.

As you can see on the attached image, WP does not show me the line with all the user roles and the counter for each role. It only shows one "ALL (0)" but there are 70,000 registered users with different roles.

Loading pages like these brings me back to a page with zero users that can not be true: http: //mydomain/wp-admin/users.php? Role = subscriber

Probably (I guess) something missing in the user_meta table but I do not know what.

I would like to force WP to rebuild the users table, but I do not know if this is possible.

Does anyone know how to deal with this problem?

Thank you

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Tracing – How to Add a Plot Legend to a Rotate Show Expression

I have a problem, the caption is displayed as a rotation and I want it in normal form
Thank you

Plotf = Labeled[Rotate[Show[R5, e2, PlotRange -> All ], 270 degrees], {"Depth m", "Residual load in kN"}, {Left, Top}, RotateLabel -> True]Show[Plotf, Epilog -> Inset[Framed[Column[{PointLegend[{Blue}, {"   Measured"}], LineLegend[{Red}, {"Estimated"}]}], RoundingRadius -> 5], Scaled[{0.8, 0.85}]]]