graphs and networks – This is a form function generation code and result of quarter singular element mesh. Is it correct?

enter image description here

enter image description here

This is a form function generation code and result of quarter singular element mesh. Is it correct?

parm = LinearSolve({f(1), f(2), f(3), f(4), f(5), f(6), f(7), 
    f(8)}, {u1, u2, u3, u4, u5, u6, u7, u8});
f(n_) = {1, Subscript(x, n ), Subscript(y, n ), Subscript(x, n )^2, 
   Subscript(x, n )*Subscript(y, n ), Subscript(y, n )^2, 
   Subscript(y, n )*Subscript(x, n )^2, 
   Subscript(x, n )*Subscript(y, n )^2};
Subscript(x, 1 ) = 1; Subscript(y, 1 ) = 1;
Subscript(x, 2) = -1; Subscript(y, 2 ) = 1;
Subscript(x, 3 ) = -1; Subscript(y, 3 ) = -1;
Subscript(x, 4 ) = 1; Subscript(y, 4 ) = -1;
Subscript(x, 5 ) = 0; Subscript(y, 5 ) = 1;
Subscript(x, 6 ) = -1; Subscript(y, 6 ) = 0;
Subscript(x, 7 ) = 0.5; Subscript(y, 7 ) = -1;
Subscript(x, 8) = 1; Subscript(y, 8 ) = -0.5;
g = Coefficient(parm, #) &;
formfuction = {g(u1), g(u2), g(u3), g(u4), g(u5), g(u6), g(u7), 
    g(u8)} . {1, x, y, x^2, x*y, y^2, y*x^2, x*y^2};
shapformfuction = formfuction /. Association({x -> r, y -> s});
Print("N(1,2,3,4,5,6,7,8)=", shapformfuction // MatrixForm)

graphs and networks – How to construct quarter point element in finite element

When calculating the stress intensity factor of a cracked body, singular elements are usually used to divide the region near the crack tip in order to meet the requirement of singularity at the crack tip. For the plane element, by folding one of the edges of the quadrilateral element and adjusting the position of the middle node of the quadrilateral element, the singular element satisfying different singularity requirements can be obtained.
The singularity of r-1/2 can be obtained at the crack tip by folding one of the elements of the second-order quadrilateral element, binding the three nodes of the folded edge together, and moving the intermediate node to the 1 / 4 position of the edge of the element.
How to generate quarter point singular element by program?

enter image description here

screen – Quarter circle with self-filling edge when mouse pointer is near the corner in Big Sur

I am new to Big Sur. While setting it up, I noticed a feature I had not seen before. Whenever the cursor got close to one of the four corners of the screen, a quarter-circle-like shape appeared adjusted to the specific corner and the edge of the quarter circle was gradually being filled up with color.

In the meantime, I have changed a lot of settings in Big Sur and I can no longer reproduce this phenomenon. As a result, I cannot post a screenshot/video and must rely on the verbal description above. If this description sounds familiar to anyone, I would be grateful for the identification of this feature. The closest match I could find is hot corners, but this quarter-circle thing definitely seems to be a distinct feature.

algorithms – Fast query on the number of elements in a quarter plane

A 2D Fenwick tree can solve this in $O(log^2 N)$ time and $O(N^2)$ space for both update and query, when your coordinates are integers and $N$ is the size of the maximum coordinate.

Fenwick trees are nice for competitive programming because they have a really compact implementation, for example in C++:

typedef unsigned long long uw;
uw lsb(uw x) { return x & -x; }
uw  up(uw x) { return x + lsb(x); }
uw  dn(uw x) { return x - lsb(x); }

template<class T> struct Fenwick2D {
  uw n; std::vector<std::vector<T>> b;
  Fenwick2D(uw n) : n(n), b(n+1, std::vector<T>(n+1)) { }

  void increase(uw x, uw y_, T v) {
    for (; x <= n; x = up(x))
      for (uw y = y_; y <= n; y = up(y))
        b(x)(y) += v;

  T prefix_sum(uw x, uw y_) {
    T s = 0;
    for (; x >= 1; x = dn(x))
      for (uw y = y_; y >= 1; y = dn(y))
        s += b(x)(y);
    return s;

And this shows your example from the question:

int main(int argc, char** argv) {
    Fenwick2D<int> fw(4);
    fw.increase(1, 1, 1);
    fw.increase(2, 2, 1);
    fw.increase(1, 2, 1);
    fw.increase(3, 2, 1);
    std::cout << fw.prefix_sum(1, 1) << "n";
    std::cout << fw.prefix_sum(2, 2) << "n";
    std::cout << fw.prefix_sum(3, 3) << "n";
    return 0;

This data structure is more general than your problem as well. In general it can increase any grid element $g_{x,y}$ by value $v$ (which decreases for negative $v$), and ask the value of the lower quadrant prefix sum $sum_{ileq x}sum_{jleq y} g_{i,j}$ for any $x, y$. Note that this means you can get area sums as well using 4 queries by the inclusion-exclusion principle.

transformation – How to scale major and minor radius of a quarter torus

I am dealing with quarter toruses as in the image below. My issue is i need to be able scale its major radius and minor radius seperately using a scale matrix. However, when i use a regular transformation matrix like:

    scaleX, 0, 0, 0,
    0, scaleY, 0, 0,
    0, 0, scaleZ, 0,
    0, 0, 0, 1;

It scales both radiuses. Is there are way i can do this seperately? I cant get my head around how this would be possible? Thank you in advance.
enter image description here

quarter rack colocation in houston,tx and/or virginia/washington dc

anyone have list of providers to look for quarter rack colocation

#1. houston, tx


#2. washington dc or virginia area

should … | Read the rest of

cheapest quarter rack colocation in the United States

i am looking for offers for the cheapest/best value quarter rack colocation in the United States

below are what am looking for but anything close to it is good, doesn’t have to be exactly that

quarter rack

10Amp @ 120V usable power

/28 ipv4 + /64 ipv6

30TB @ 1 Gbps port

the economy is heading downhill and trying to reduce costs as last resort

so please reply with the cheapest providers out there or DM also

looked at colo offers section but nothing catches my eyes in terms of price

again don’t care what location, just want cheapest price possible


Linux: 1080p external screen desktop only covers a quarter screen [Using xrandr]

I used to use Ubuntu for my development environment, since I have a new workstation that I have decided to switch to Manjaro, with a KDE GUI.

When I used Gnome, I used a tool called xrandr-extend to give me the ability to use both the 4k screen of my laptop and my external 1080p screen without suffering from the usual scaling problems. It works well; I had no problems with xrandr-extend in Gnome. In Manjaro, however, I have a problem that I cannot solve.

The problem lies in the desktop on the external screen:

Desk with external display

As you can see, three quarters of the screen are black, while the desk accommodates the last quarter of the screen.

I think it may have something to do with the fact that I am compressing the screen by 2 in the xrandr-extend configuration. I am doing this to achieve the optimum degree of scale to use applications on the screen. However, if this is the case, how can I maintain the level of scale that I need while the entire desktop instance on the external screen covers the entire width and length of that screen?

To my knowledge, I have filled in the configuration file correctly:

primary = eDP-1
hdmi = HDMI-1
vga = DP-1

primary = eDP1
hdmi = HDMI1
vga = DP1

primary = 3840, 2180
hdmi = 1920, 1080
vga = 1920, 1200

hdmi =  2

The console logs generated when I execute the command to extend and scale the external screen:

[dukejm@duke-pc ~]$ xrandr-extend -n hdmi                 
xrandr --auto
xrandr --listmonitors
xrandr --output eDP1 --auto --output HDMI1 --auto --panning 3840x2160+3840+0 --scale 2.0x2.0 --right-of eDP1
Monitors: 2
 0: +*eDP1 3840/350x2160/190+0+0  eDP1
 1: +HDMI1 1920/530x1080/300+3840+0  HDMI1
[dukejm@duke-pc ~]$ xrandr-extend -n hdmi
xrandr --auto
xrandr --listmonitors
xrandr --output eDP1 --auto --output HDMI1 --auto --panning 3840x2160+3840+0 --scale 2.0x2.0 --right-of eDP1
Monitors: 2
 0: +*eDP1 3840/350x2160/190+0+0  eDP1
 1: +HDMI1 3840/530x2160/300+3840+0  HDMI1

Google Calendar: How to add a school schedule (explaining the lack of lessons between the dates of the quarter)?

I am trying to add my school schedule to the Google calendar, but the weekly replay options do not explain that there are no lessons between the terms. Nor have I found a way to eliminate multiple events at once (i.e., vacation lessons)

Thanks for any help.

Facebook ad rates have risen in the fourth quarter of 2017 |

Facebook ad rates have risen in the fourth quarter of 2017.

Let's talk about why and some solutions to avoid wasting your Facebook ad dollars.

During the fourth quarter of each year, we see an increase in ad rates on the Facebook ad platform.

The reason for this is that we have more people spending money during this time of year, which attracts more companies to the market.

Facebook ad auctions are filled with people looking to bid on ad inventory, and are also willing to pay the maximum to access the inventory.
As a result, ad rates rise in all areas.

You have some solutions to this challenge.
1. Know your numbers. You have to know your cold numbers. Knowing your CPA, LTV and even AOY is essential at this time of year
2. Create attractive offers Creating a compelling offer is key. Try to find out what your customer really wants and how you can make him act on the offers.
3. Test your assumptions. Start testing all your assumptions with a part of your budget. Then try again.

The change in Facebook's fourth quarter ad rate is preparing us for higher ad rates in 2018.

Get ready and get ready.