Number Theory – Small solutions for linear simultaneity ratio of diophantines

Suppose I have integers $ a_1, …, a_n $ Which are Koprime, that is

$$ a_1 b_1 + … + a_n b_n = 1 $$

has a solution in whole numbers $ b_1, …, b_n $, I would like to get a hard-coded proverb

There is a solution with $ sum_i | b_i | < sum_i | a_i | $ (except in the degenerate case where $ a_j = 1 $, $ a_i = 0 $ to the $ i neq j $)

Presumably, such things (and probably much stronger borders) are known. Does anyone know a reference for these types of results?

Touchscreen Ghost Touch Solution – Method to prevent a small portion of the screen from being touch-sensitive?

So I ordered a cheap Chinese phone (umidigi) as a secondary device, and the device I got out of home was plagued with a faulty display. When troubleshooting, I've diagnosed the problem accurately:

  • There is an irregular incorrect input in the lower right corner of the screen
  • Decreasing the brightness seems to minimize the presence of the wrong input
  • The device may need to be disassembled to fix the problem

I notified the seller where I bought the phone and they send me a new unit. Yay.

So in the end, I want to solve this problem permanently and open it myself, but in the meantime, I want to use some of it. But with the Ghost Touch it is crazy to operate the phone with something other than a Bluetooth mouse.

The affected area is at the very end of the phone and can not exceed 15 pixels. I tried to use some apps, one called "Partial Screen" and some others like Screen Shift. However, the adjustments to the display only result in cosmetic changes and do not desensitize the adjusted portion of the screen to touch the input, causing problems with the wrong input.

Can someone point me to a procedure, adb input or otherwise, that could ensure that a certain area of ​​the touch screen does not consider touch input?

Many Thanks.

Looking for a very small, unmanaged VPS


I need a very small unmanaged VPS. It would be absolutely sufficient for me to have 256 MB RAM and 3 GB HDD. This VPS is needed to organize a slave name server in the US – this is the preferred VPS location for me. I do not know how much such VPS could cost, but I think rather cheap.

Thank you in advance.

What is the best project management or organization software for small businesses?

Device recommendation – Which camera shoulder bag should be chosen for small DSLR cameras with 2-3 additional lenses and flashlight?

I would like to buy a camera shoulder bag to mount a small DSLR camera with attached lens, 2-3 additional lenses and a flash.

The choice of lenses I want to wear may vary depending on the situation, but at least I want to be able to wear this option with one lens attached to the camera and two or three other lenses that carry the lens caps on both sides:

  1. Zoom, Telezoom and 50mm
    • Canon 55-250 mm
    • Canon 18-55mm
    • Canon 50mm 1: 1.8
  2. Many zooms
    • Canon 55-250 mm
    • Canon 18-55mm
    • Canon 10-18 mm
  3. Primes and Ultrawide
    • Canon 24mm 1: 2.8 (Pancake Lens)
    • Canon 50mm 1: 1.8
    • Canon 85mm 1: 1.8
    • Canon 10-18 mm

Note that 50mm and 24mm together are the size of a zoom lens. Although one of the lenses has 4 lenses, it still counts as 3 in practice.

I also have a small DSLR (Canon 2000D) and a flash (Canon 430EX-III RT). I also ordered a MagMod MagGrip and a MagMod MagBounce.

I have several criteria:

  • Weather protection is a must
  • The weight of the bag should be reasonably low (I expect the shoulder bag to increase the maximum total weight to 2.6-2.8 kg, depending on the weight of the bag when using Lens Selection 3, the flash and MagMod equipment I hate weighty equipment, I temporarily carried a laptop in a shoulder bag with a total weight of 3.5 kg, which is a bit uncomfortable, therefore 2.6 – 2.8 kg should be hardly acceptable his.)
  • Should be permanent
  • Should not be too big in the outside dimensions; no "future expansion" is required as the amount of equipment I can carry is limited by weight anyway

My research has convinced me that the Nova 160 AW II and 170 AW II of the Lowepro bags are too small. So I have to buy the Nova 180 AW II when I take a Lowepro bag.

Can someone recommend which bag to choose? Is my estimate correct that Nova 180 AW II would be necessary? Is there another good choice than Lowepro?

One option would be to go to a retailer who has several Lowepro bags on the shelf and try to fit all the equipment in the bag. However, this is complicated by two things: (1) The 10-18mm and MagMod devices I ordered. Not yet arrived, (2) one of the retailers where I often buy things has no 170 AW II on the shelf so I can not try all three.

I will not use the bag for traveling abroad. If I travel to another country one day and wear a DSLR for the trip, I'll buy another smaller camera bag for the trip.

To draw a complex scene diagram with many lines, "dots" (small circles), polygons, curves, and images in WebGL

For example, the pictures below show some of the complexity of the drawing that might be in the game. They include complex lines and points as in diagram drawings, high-resolution images such as directly from a DSLR camera in HDR and basic vector drawings. All this in 2D, so no need for 3D light cards and the like, although in 2D there will probably be shadows and reflections in the game.

Note that the images are displayed with the complex lines / curves / points Not Images or textures are actual WebGL lines / curves / points.

My question is what features of WebGL I have to use for this. Especially the to draw Making calls because I'm not sure if I should use anything else gl.TRIANGLES when drawing or when there is a use case for gl.LINES or others.

My previous understanding is that I basically have to do it these for images (not sure if this is how high-resolution images work, still wondering about it):

var texture = gl.createTexture ()
gl.bindTexture (gl.TEXTURE_2D, texture)

gl.texParameteri (gl.TEXTURE_2D, gl.TEXTURE_WRAP_S, gl.CLAMP_TO_EDGE)
gl.texParameteri (gl.TEXTURE_2D, gl.TEXTURE_WRAP_T, gl.CLAMP_TO_EDGE)
gl.texParameteri (gl.TEXTURE_2D, gl.TEXTURE_MIN_FILTER, gl.NEAREST)
gl.texParameteri (gl.TEXTURE_2D, gl.TEXTURE_MAG_FILTER, gl.NEAREST)

gl.texImage2D (gl.TEXTURE_2D, 0, gl.RGBA, gl.RGBA, gl.UNSIGNED_BYTE, image)

A color buffer for the vector colors:

var colorBuffer = gl.createBuffer ()
gl.bindBuffer (gl.ARRAY_BUFFER, colorBuffer)
gl.bufferData (gl.ARRAY_BUFFER, colors, gl.STATIC_DRAW)
gl.vertexAttribPointer (1, 3, gl.FLOAT, false, 0, 0)
gl.enableVertexAttribArray (1)

A vertex and index buffer and a texture buffer for the images above.

gl.bindBuffer (gl.ARRAY_BUFFER, vertexBuffer)
gl.bufferData (gl.ARRAY_BUFFER, 12 * sizeof (float), positions, gl.STATIC_DRAW)
gl.bindBuffer (gl.ARRAY_BUFFER, 0)

gl.bindBuffer (gl.ARRAY_BUFFER, colorBuffer)
gl.bufferData (gl.ARRAY_BUFFER, 16 * sizeof (float), colors, gl.STATIC_DRAW)
gl.bindBuffer (gl.ARRAY_BUFFER, 0)


gl.bindBuffer (gl.ELEMENT_ARRAY_BUFFER, indexBuffer)
gl.bufferData (gl.ELEMENT_ARRAY_BUFFER, sizeof (ushort), indices, gl.STATIC_DRAW)

And then they draw:

gl.drawArrays (gl.TRIANGLES, 0, 3)
// or for indexes:
gl.drawElements (gl.TRIANGLES, 4, gl.UNSIGNED_SHORT, 0)

I'm not sure how to do that drawArrays (gl.TRIANGLES, ...) and drawElements (gl.TRIANGLES, ...), Given the limitations above, I wonder if I want always just use it TRIANGLESor if I would like to use one of the variants LINES or TRIANGLE_FAN or something else. That's basically my question, for each of these situations, what kind of call should I make and why.

1 complex lines and points

(ignore the color gradients, no color gradients are displayed)

Enter the image description here

2 more lines and points

Enter the image description here

3 detailed pictures in high resolution

Enter the image description here

4 vector-like characters

Enter the image description here

xfce – Redshift Gamma ramp size too small: 0 Error while starting the adaption method randr

I use Linux Mint 18.3, it is Ubuntu 16.04 base

in my thinkpad t480 (laptop has nvidia card), the redshift works fine

but in my dell optiplex 3060m (desktop pc has only intel gpu), the redshift does not work:

Gamma ramp size too small: 0
Failed to start fitting method randr.

How can I fix this?