## Equation Resolution – Is it possible to use FindRoot with a two variable function?

Thank you for your contribution to Mathematica Stack Exchange!

• Please make sure to respond to the question. Provide details and share your research!

But to avoid

• Make statements based on the opinion; save them with references or personal experience.

Use MathJax to format equations. MathJax reference.

I came across this issue on different forums where Google uses our answer when resolving reCAPTCHA to drive its artificial intelligence. For example, some say that spotting stop signs and cars in reCAPTCHA drives Google's standalone AI. I am not sure of the authenticity of these claims, but I doubt that it is even theoretically possible to train an AI this way.

ReCAPTCHA asks the user to locate or identify a certain thing and, by answering it incorrectly, asks you to try again. This means that Google already has the knowledge of the correct answers to the challenge. He already knows what pictures are stop signs and cars. Is not it enough to train an AI? Why is my contribution to the puzzle necessary to train the AI?

## group theory gr. – resolution of auther cayley for the quintic equation

hello i want to get different numbers using cayley resolvent

and I put integers x1 = 1 x2 = 2 x3 = 3 x4 = 4 x5 = 5

when to swap the integers in

= (X1x2 + x2x3 + x3x4 + x4x5 + x5x1
-X1x3 -x3x5 -x5x2 -x2x4 -x4x1) ^ 2

I've had (1,25,81,121) four digits but I'm not sure
is this the right way to think such a resolute?

## real analysis – Resolution for a monotonic function – contraction operator for functions?

I want to solve a problem for a increasing function $$g (x)$$, for $$x in [0,1]$$ and with $$g (0) = 0$$ and $$g (1) = 1$$.
The solution will be the solution to the following equation
$$forall x$$, $$f_1 (x) = f_2 (g (x))$$.
(with $$f_1$$ and $$f_2$$ known)

however, $$f_2$$ may not be invertible (it is, however, monotonous in pieces). So for some people $$x$$, you have multiple solution $$g (x)$$, which we will note $$(g ^ 1 (x), g ^ 2 (x), …, g ^ k (x))$$ (Given the structure of the problem, you still have a countable number of solutions).

However, overall, there is a unique solution growing $$g ^ * ()$$ of $$[0,1] right arrow [0,1]$$.
My problem is, I do not know how impose the constraint of monotony when solving a system, so I should be able to pinpoint the unique solution "directly" (I do not know if this is even possible).
Or in other words, I do not know the tricks to write the system with the integrated monotony, solve for the full function $$g ()$$, instead of solving by points $$x$$ by $$x$$.

I was trying to build a contraction mapping operator (maybe that's not the way to go), but I have to integrate the monotonicity constraint in the contraction operator and I do not know how to do that. (Because taken to a given $$x$$, our system can give several solutions and therefore no contraction mapping is feasible).

PS: Just to be clear, in this particular case, I know how to encircle $$g ()$$ exploiting piecewise monotony entirely (and thus building piece-wise invertibility). My question is actually about tips for including monotony in a system (as an additional equation? Constraint?) And, if possible, using a contraction mapping with it.

## How to adapt the WindowsForm form to any screen resolution, C #?

I want to adapt the form with its respective buttons to any screen resolution. Thank you

## graphs – Resolution of the minimum edge coverage using the maximum matching algorithm

To resolve an edge coverage instance, we can use the maximum matching algorithm.

Edge cover: A chart's edge cover is a set of edges such that each vertex of the chart is incident on at least one edge of the set [from Wikipedia].

Maximum correspondence: a corresponding or independent edge defined in a graph is a vertex without common vertices [from Wikipedia].

For example, to find the minimum edge coverage of the example below, we can:

1- Find a maximum match.

2- The extension greedily so that all the summits are covered.

The image below shows this solution:

My question is why this reduction works, is there any evidence of this result? or at least an intuition!

How can one be sure that the final solution is the minimal edge coverage of the chart and that there is no other edge coverage smaller than the calculated solution?

## super-resolution – how to create a very high resolution photo for wallpaper

I'm building a house right now.

North of the house there is a forest.

I wanted to create a very high resolution photo of the forest to create a screen background (carpet? What is the correct English word, large scale printing to stick to the wall). I do not have a window on the north side.

It would be more than 10 meters wide, so I would need a high resolution.

I do not want a panorama with visible distortion.

In addition, as the forest is quite close (see photo attached from the roof, cropping a panorama, in winter, I would take the picture in summer).

What would be the appropriate method to create such an image?
Focus Stacking + Image Stacking to create a super-resolution solution?
Would I take pictures of several fists parallel to the edge of the forest to counter the distortions?

Available material:
Sony a6000
Sony a7 (friends)
different high quality lenses with different focal lengths
Gigapan Epic Pro Automated Panorama Head

Thank you
Daniel

## 60×40 canvas print and resolution

I would like to know what resolution do I need to print a 60×40 canvas? I would place the canvas print about 7 feet high and be seen about 10 feet away. Is the 4082 x 2836 resolution sufficient?

## ffmpeg capture from uvc / dev / video0 in any resolution, EXCEPT 1920×1080

Basically, the problem is that ffmpeg will not capture 1920×1080 on my Linux system, unlike other video capture applications, and yet ffmpeg will successfully capture other resolutions from the same device on the same system. Bizarre. I have tried many combinations of ffmpeg command lines and muttered many incantations, but none of them solves the problem.

I'm using ffmpeg on the 19.04 Ubuntu desktop on a 2200g Ryzen with 16 GB of RAM.

My goal is to create a H264 mp4 video that can be viewed in a web browser, with data from a USB UVC device. The resulting file should be read correctly in the quicktime player on Windows and in a web browser.

• Fact 1: I have a HDMI device UVC to USB capable of 4K video
contribution.
• Fact 2: ffmpeg works correctly when I capture a video with the help of ffmpeg in any
resolution EXCEPT 1920×1080
• Fact 3: ffmpeg also works very well by capturing the 4k input as well as all
lower resolutions
• Fact 4: gstreamer seems to be able to capture data – he has created a
gigantic file (see annex 1 below)
• Fact 5: The guvcview program on the Ubuntu desktop has no problem
display the video from the uvc device and does not require any
configuration to do it.
• Fact 6: I used the guvcview program on the Ubuntu desktop in command line mode
capture the video of the uvc camera in 1920×1080 and processed it
well

######## Appendix 1: uvc devices

ubuntu @ render001: ~ $ls / dev / vid * / dev / video0 / dev / video1 ######## Appendix 2: UVC Device Information ubuntu @ render001: ~$ v4l2-ctl --all
Driver info:
Driver name: uvcvideo
Bus Information: usb-0000: 08: 00.3-4
Driver Version: 5.0.8
Capacities: 0x84a00001
Video capture
Diffusion
Extended Pix format
Capacities of the device
Device Caps: 0x04200001
Video capture
Diffusion
Extended Pix format
Priority: 2
Video input: 0 (input 1: ok)
Format the video capture:
Width / Height: 1920/1080
Pixel format: YUYV & # 39; (YUYV 4: 2: 2)
Field: none
Bytes per line: 3840
Size: 4147200
Color space: sRGB
Transfer function: default (mapped to sRGB)
YCbCr / HSV encoding: default (maps to ITU-R 601)
Quantization: default (mapped to a limited range)
flags:
Video capture of the ability to crop:
Bounds: Left 0, Top 0, Width 1920, Height 1080
Default: Left 0, Top 0, Width 1920, Height 1080
Aspect of the pixel: 1/1
Selection: crop_default, Left 0, Top 0, Width 1920, Height 1080, Flags:
Selection: crop_bounds, Left 0, Top 0, Width 1920, Height 1080, Flags:
Streaming Video Capture Settings:
Capabilities: timeperframe
Frames per second: 60,000 (60/1)
brightness 0x00980900 (int): min = 0 max = 255 steps = 1 default = 128 value = 128
contrast 0x00980901 (int): min = 0 max = 255 steps = 1 default = 128 value = 128
saturation 0x00980902 (int): min = 0 max = 255 steps = 1 default = 128 value = 128
hue 0x00980903 (int): min = 0 max = 255 steps = 1 default = 128 value = 128

######## Appendix 3: ffmpeg case exit failed

ubuntu @ render001: ~ $ffmpeg -y -t 5 -f video4linux2 -i / dev / video0 out.mov Ffmpeg Version N-94046-gc9c1711 Copyright (c) 2000-2019 the developers of FFmpeg built with gcc 8 (Ubuntu 8.3.0-6ubuntu1) configuration: --prefix = / home / ubuntu / ffmpeg_build --pkg-config-flags = - static --extra-cflags = -I / home / ubuntu / ffmpeg_build / include --extra-ldflags = -L / home / ubuntu / ffmpeg_build / lib --extra-libs = - lpthread -lm & # 39; --bindir = / home / ubuntu / bin --enable-lib - libable - libable - libable - libable - libable -libvpx --enable-libx264 --enable-libx265 --enable-nonfree libavutil 56. 28.100 / 56. 28.100 libavcodec 58. 53.100 / 58. 53.100 libavformat 58. 27.103 / 58. 27.103 libavdevice 58. 7.100 / 58. 7.100 libavfilter 7. 55.100 / 7. 55.100 libswscale 5. 4.101 / 5. 4.101 libswresample 3. 4.100 / 3. 4.100 libpostproc 55. 4.100 / 55. 4.100 ****** IMPORTANT NOTE ***** ffmpeg hangs at this point and the following display is displayed after pressing C: Entry # 0, video4linux2, v4l2, from / dev / video0: Duration: N / A, speed: 1492992 kb / s Stream # 0: 0: Video: rawvideo (I420 / 0x30323449), yuv420p, 1920x1080, 1492992 kb / s, 60 frames per second, 60 tbr, 1000 kb tb, 1000k tbc Flow Mapping: Stream # 0: 0 -> # 0: 0 (rawvideo (native) -> h264 (libx264)) press [q] Stop, [?] to help Workflow 0: 0 without any written data. [libx264 @ 0x55efe29a1c00] CPU capacity utilization: MMX2 SSE2Fast SSSE3 SSE4.2 AVX FMA3 BMI2 AVX2 [libx264 @ 0x55efe29a1c00] profile High, level 4.2 [libx264 @ 0x55efe29a1c00] 264 - core 155 r2917 0a84d98 - H.264 / MPEG-4 AVC codec - Copyleft 2003-2018 - http://www.videolan.org/x264.html - options: cabac = 1 ref = 3 unlocking = 1: 0: 0 analysis = 0x3: 0x113 me = subword hex = 7 psy = 1 psy_rd = 1.00: 0.00 mixed_ref = 1 me_range = 16 chroma_me = 1 lattice = 1 8x8dct = 1 cqm = 0 deadzone = 21.11 fast_pskip = 1 chroma_qp_offset = -2 threads = 6 lookahead_threads = 1 sliced_threads = 0 nr = 0 decimal = 1 interlace = 0 bluray_compat = 0 constrained_intra = 0 bframes = 3 b_pyramid = 2 b_adapt = 1 b_bias = 0 direct = 1 bbp = 1 open_gop = 1 open_gop = 1 open_gop = 1 250 keyint_min = 25 scenecut = 40 intra_refresh = 0 rc_lookahead = 40 rc = crf mbtree = 1 crf = 23.0 qcomp = 0.60 qpmin = 0 qpmax = 69 qpstep = 4 ip_ratio = 1.40 aq = 1: 1.00 Exit # 0, mov, to & # 39; out.mov & # 39 ;: metadata: encoder: Lavf58.27.103 Stream # 0: 0: Video: h264 (libx264) (avc1 / 0x31637661), yuv420p, 1920x1080, q = -1-1, 60 frames per second, 15360 billion yuan, 60 frames per second metadata: encoder: Lavc58.53.100 libx264 Lateral data: cpb: bitrate max / min / avg: 0/0/0 size of the buffer: 0 vbv_delay: -1 frame = 0 fps = 0.0 q = 0.0 Lsize = 0kB time = 00: 00: 00.00 bit rate = N / A speed = 0x video: 0 ko audio: 0 kb subtitle: 0 kb other streams: global headers 0 kb: 0 kb multiplexing overhead: unknown Normal output, received signal 2. ubuntu @ render001: ~$

######## Appendix 4: the successful ffmpeg case output – not here that the

Only difference was that the resolution of the input in the UVC device was changed to 3840x2160. The output .mov file is read correctly in the Quicktime Player or in a browser.

ubuntu @ render001: ~ $ffmpeg -y -t 5 -f video4linux2 -i / dev / video0 out.mov Ffmpeg Version N-94046-gc9c1711 Copyright (c) 2000-2019 the developers of FFmpeg built with gcc 8 (Ubuntu 8.3.0-6ubuntu1) configuration: --prefix = / home / ubuntu / ffmpeg_build --pkg-config-flags = - static --extra-cflags = -I / home / ubuntu / ffmpeg_build / include --extra-ldflags = -L / home / ubuntu / ffmpeg_build / lib --extra-libs = - lpthread -lm & # 39; --bindir = / home / ubuntu / bin --enable-lib - libable - libable - libable - libable - libable -libvpx --enable-libx264 --enable-libx265 --enable-nonfree libavutil 56. 28.100 / 56. 28.100 libavcodec 58. 53.100 / 58. 53.100 libavformat 58. 27.103 / 58. 27.103 libavdevice 58. 7.100 / 58. 7.100 libavfilter 7. 55.100 / 7. 55.100 libswscale 5. 4.101 / 5. 4.101 libswresample 3. 4.100 / 3. 4.100 libpostproc 55. 4.100 / 55. 4.100 Entry # 0, video4linux2, v4l2, from / dev / video0: Duration: N / A, start: 625.791663, speed: 2985984 kb / s Feed # 0: 0: Video: rawvideo (I420 / 0x30323449), yuv420p, 3840x2160, 2985984 kb / s, 30 frames per second, 30 tbr, 1000 000 tbn, 1000 000 tbc Flow Mapping: Stream # 0: 0 -> # 0: 0 (rawvideo (native) -> h264 (libx264)) press [q] Stop, [?] to help [libx264 @ 0x5586ca510300] CPU capacity utilization: MMX2 SSE2Fast SSSE3 SSE4.2 AVX FMA3 BMI2 AVX2 [libx264 @ 0x5586ca510300] profile High, level 5.1 [libx264 @ 0x5586ca510300] 264 - core 155 r2917 0a84d98 - H.264 / MPEG-4 AVC codec - Copyleft 2003-2018 - http://www.videolan.org/x264.html - options: cabac = 1 ref = 3 unlocking = 1: 0: 0 analysis = 0x3: 0x113 me = subword hex = 7 psy = 1 psy_rd = 1.00: 0.00 mixed_ref = 1 me_range = 16 chroma_me = 1 lattice = 1 8x8dct = 1 cqm = 0 deadzone = 21.11 fast_pskip = 1 chroma_qp_offset = -2 threads = 6 lookahead_threads = 1 sliced_threads = 0 nr = 0 decimal = 1 interlace = 0 bluray_compat = 0 constrained_intra = 0 bframes = 3 b_pyramid = 2 b_adapt = 1 b_bias = 0 direct = 1 bbp = 1 open_gop = 1 open_gop = 1 open_gop = 1 250 keyint_min = 25 scenecut = 40 intra_refresh = 0 rc_lookahead = 40 rc = crf mbtree = 1 crf = 23.0 qcomp = 0.60 qpmin = 0 qpmax = 69 qpstep = 4 ip_ratio = 1.40 aq = 1: 1.00 Exit # 0, mov, to & # 39; out.mov & # 39 ;: metadata: encoder: Lavf58.27.103 Stream # 0: 0: Video: h264 (libx264) (avc1 / 0x31637661), yuv420p, 3840x2160, q = -1-1, 30 frames per second, 15360 tb, 30 frames / second metadata: encoder: Lavc58.53.100 libx264 Lateral data: cpb: bitrate max / min / avg: 0/0/0 size of the buffer: 0 vbv_delay: -1 image = 151 frames / second = 18 q = -1.0 Actual size = 476 KB time = 00: 00: 04.93 bit rate = 791.1 kbit / s dup = 11 drops = 0 rate = 0.588x video: 474ko audio: 0ko subtitle: 0ko other streams: global headers 0k: 0ko multiplexing overhead: 0.538915% [libx264 @ 0x5586ca510300] Size I: 1 Average QP: 19.12 Height: 115507 [libx264 @ 0x5586ca510300] frame P: 38 average QP: 18.89 size: 6063 [libx264 @ 0x5586ca510300] frame B: 112 average PQ: 21.48 size: 1238 [libx264 @ 0x5586ca510300] consecutive B images: 0.7% 1.3% 0.0% 98.0% [libx264 @ 0x5586ca510300] mb I I16..4: 23.5% 70.7% 5.8% [libx264 @ 0x5586ca510300] mb P I16..4: 0.1% 0.1% 0.0% P16..4: 9.8% 0.0% 0.3% 0.0% 0.0% skip: 89.6% [libx264 @ 0x5586ca510300] mb B I16..4: 0.0% 0.0% 0.0% B16..8: 2.6% 0.0% 0.0% direct: 0.0% skip: 97.4% L0: 34.6% L1: 65.4% BI: 0.0% [libx264 @ 0x5586ca510300] Intra 8x8 transformation: 69.0% inter: 99.8% [libx264 @ 0x5586ca510300] y-coded, uvDC, uvAC intra: 21.6% 55.2% 9.8% inter: 0.4% 3.0% 0.0% [libx264 @ 0x5586ca510300] i16 v, h, dc, p: 56% 32% 7% 5% [libx264 @ 0x5586ca510300] i8 v, h, dc, ddl, ddr, vr, hd, vl, hu: 39% 10% 42% 2% 2% 1% 2% 1% 1% 1% [libx264 @ 0x5586ca510300] i4 v, h, dc, ddl, ddr, vr, hd, vl, hu: 41% 12% 21% 7% 5% 4% 5% 5% 1% [libx264 @ 0x5586ca510300] i8c dc, h, v, p: 60% 25% 14% 2% [libx264 @ 0x5586ca510300] Weighted P-frames: Y: 0.0% UV: 0.0% [libx264 @ 0x5586ca510300] ref P L0: 81.0% 0.3% 15.1% 3.6% [libx264 @ 0x5586ca510300] ref B L0: 68.4% 31.5% 0.2% [libx264 @ 0x5586ca510300] ref B L1: 99.5% 0.5% [libx264 @ 0x5586ca510300] kb / s: 770.14 ubuntu @ render001: ~$

######## Appendix 7: Successful gstreamer case exit

ubuntu @ render001: ~ $gst-launch-1.0 -v device v4l2src = / dev / video0! video / x-raw, number of frames per second = 60/1, width = 1920, height = 1080! location of the file = gopro2.mp4 Setting the pipeline on PAUSED ... The pipeline is energized and does not need PREROLL ... Setting the pipeline to PLAY ... New clock: GstSystemClock /GstPipeline:pipeline0/GstV4l2Src:v4l2src0.GstPad:src: caps = video / x-raw, framerate = (fraction) 60/1, width = (int) 1920, height = (int) 1080, format = (string) YUY2 , format-pixel = (fraction) 1/1, colorimetry = (string) bt709, interlaced mode = (progressive) /GstPipeline:pipeline0/GstCapsFilter:capsfilter0.GstPad:src: caps = video / x-raw, framerate = (fraction) 60/1, width = (int) 1920, height = (int) 1080, format = (string) YUY2 , format-pixel = (fraction) 1/1, colorimetry = (string) bt709, interlaced mode = (progressive) /GstPipeline:pipeline0/GstFileSink:filesink0.GstPad:sink: caps = video / x-raw, framerate = (fraction) 60/1, width = (int) 1920, height = (int) 1080, format = (string) YUY2 , format-pixel = (fraction) 1/1, colorimetry = (string) bt709, interlaced mode = (progressive) /GstPipeline:pipeline0/GstCapsFilter:capsfilter0.GstPad:sink: caps = video / x-raw, framerate = (fraction) 60/1, width = (int) 1920, height = (int) 1080, format = (string) YUY2 , format-pixel = (fraction) 1/1, colorimetry = (string) bt709, interlaced mode = (progressive) ^ Stop Chandling. Interruption: pipeline stop ... The run is over after 0: 00: 02.464259973 Setting the pipeline on PAUSED ... Setting the pipeline to READY ... Defining the pipeline on NULL ... Free the pipeline ... ubuntu @ render001: ~$ ls -lah gopro2.mp4
-rw-rw-r-- 1 ubuntu ubuntu 550M Jun 16 12:33 PM gopro2.mp4
ubuntu @ render001: ~ $######## Appendix 7: the successful guvcview case output ubuntu @ render001: ~$ guvcview --device = / dev / video0 --video =. / guvcoutput.mkv --video_timer = 5 --exit_on_term --verbosity = 10
GUVCVIEW: version 2.0.6
GUVCVIEW: language catalog => dir: / usr / share / locale type: en_AU.UTF-8

the full (long) log output continues here: https://pastebin.com/7UArCpMv

############################ possibly useful ffmpeg info?

https://pastebin.com/WqahRxdY

## The recaptcha v2 resolution failed – no resolution of orecaptcha v2 is enabled.

I see error messages "The resolution of recaptcha v2 failed – no resolution of orecaptcha v2 is enabled" in the logs, sometimes I have enabled 2captcha in SER, and the ls # 39; balance is also sufficient.
What does it mean? and how to solve it?