The bit representation of the hash multiplication method

In the CLRS image below, I don't understand why exactly $ h (k) $ = the $ p $ higher order parts of the lower w-bit Half of the product.

For context, this is supposed to compute
$ h (k) = lfloor m (k A ; text {mod} 1) rfloor $

enter the image description here


For more context, CLRS mentions the following, but I still don't understand why those $ p $ higher order The bits are what we are looking for.

enter the image description here

linear algebra: inverse problem with the attached method.

I am trying to recreate a solution in this.

Given a wave function, I need to find the potential V (x).

Post image

From that file, it is mentioned that I need to connect the g and dg / dV in some optimization algorithm, eg nonlinear conjugate gradient.

enter the image description here

But, after checking what the nonlinear conjugate gradient does, solve Ax = B for x, which is psi in this case. Why would you want to solve psi? I already have psi. I'm sure I'm cheating here. I appreciate if someone can show me the way or point out my mistakes.

Note:
I am studying about the reverse design problem for photonic devices.
From published photonic works, I gathered 2 methods used in this photonic application, adjunct method and conjugate gradient. I have no prior knowledge of optimization (only linear algebra undergraduate), so if the title is not correct please let me know.

magento2.3 – Magento 2: Error not detected: methods cannot be called in modal before initialization; tried to call method & # 39; show & # 39;

I am using the following code to display modal, I am using the semantic user interface, I get the following error

** **

Uncaught Error: cannot call methods on modal prior to initialization; attempted to call method 'show'
    at Function.error (jquery.js:259)
    at HTMLDivElement. (widget.js:186)
    at Function.each (jquery.js:376)
    at jQuery.fn.init.each (jquery.js:142)
    at jQuery.fn.init.$.fn. (as modal) (widget.js:182)
    at :4:32
    at Object.execCb (require.js:1650)
    at Object.context.execCb (resolver.js:145)
    at Module.check (require.js:866)
    at Module.enable (require.js:1143)

** **

My code

 require((
            'jquery','semantic/minjs'
            ), function($,semantic) {            
                $('.ui.modal').modal('show');
            }
        );

c # – Design pattern when base class supports new method overload

The base class (in the lib base, which is not my property), has updated its code and added a new method that supports additional use cases.

Signature of existing method in base class

public void Alert(string someAlertString);

With the new version, the base class supports an AlertObject list (at some point, the base class could depress the string alert)

public void Alert(List alertObj);

The base class in lib looks like this:

public BaseClass {
   public void Alert(string message) {
     //Print msg on the UI.
   }

   public void Alert(List alerts) {   <-- New Addition.
     // Loop through each alert and show the list of messages.
   }

   // Other methods.
}

On my side of the code, I have the alert in multiple places in multiple subclasses (> 500 alerts), like so:

public SubClass: BaseClass {

    public void Execute(){
       // Execute some logic
       Alert("This is a warning message."); <-- Call base calls alert
    }
 }

I want to update all these alert statements to use an AlertObject (and I want to add a category only to new alerts, old alerts can continue to use the default category):

public class Alert {
   public string message {get;set;}
   public string category {get;set;}
}

One way to do this is to define a helper class that takes the existing string and returns an AlertObject List:

public static class AlertHelper {
   public static List getNewAlert(string msg, string category="Not Defined") {
      Alert a = new Alert();
      a.message = msg;
      a.category = category;
      return new List() { a };
   }
}

So I can replace the entire instance of my Alert with -

base.Alert(AlertHelper.getNewAlert("This is a warning message."))

The only problem I see here is that as the Alert class (in a separate library) keeps adding properties to support more detailed alerts, I need to keep updating my helper class and potentially all the places where I call the helper class.

I was wondering if there is a better way to design this.

php – Reloads part of the purchase in the modified shipping method

So I added the following action to add additional content about & # 39; local pickup & # 39; to the payment page.

add_action( 'woocommerce_review_order_before_payment', 'my_custom_action', 20 );

When I change the shipping method, I want to "reload" the action to hide / show content in case the shipping method is a local pickup.

I am not an expert in hooks or wordpress ajax … I cannot understand this

finite element method – FEM: electric field between two arbitrarily defined forms

I was wondering how to do the following:
I would like to calculate the electrostatic field between two ways using the FEM method.

(*Define Boundaries*)
air = Rectangle({-3, -3}, {3, 3});
object1 = Disk();
object2 = Rectangle({2, 0}, {2.5, 2});
Show(Graphics({Blue, air}), Graphics({Magenta, object1}),Graphics({Green, object2}))

enter the image description here

Calculation of the electric field at each point {x, y} in 2D space:

enter the image description here
$ r_i $ is the vector of the point charge; $ r $ is the vector to the point in 2D space (or also 3D) where we want to calculate the electric field.

I do a Mathematica function (for the moment I omit the constant term):

eField(x_, y_) := q Sum(({x, y} - pts((i)))/Norm({x, y} - pts((i)))^3, {i, n})

where pts((i)) are the limit points of the loaded object and x Y y are coordinates of the "air" object.

How it would proceed:

  1. I calculate the electrostatic field of object 1 -> $ E_1 $

  2. I calculate the electrostatic field of object 1 -> $ E_2 $

  3. I use superposition to get the resulting electric field: $ E_ {Total} = E_1 + E_2 $

I would really appreciate if someone could show me how to do it in Mathematica using Finite Element (FEM).

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Can we use js knockout as a method / approach for some functionality or solution, instead of using simple jQuery with long timeout?

Can we use js knockout as a method / approach for some functionality or fix, instead of using simple jQuery with long timeout set to keep observing behavior / clicks on checkout page?

Java: a simple method with a return statement inside a loop

I am new to programming and would like to know if I will continue looping even if it returns false?

    boolean boardIsFull(char() board){
        for(char mark : board){
            if(mark == EMPTY){ return false; }
        }
        return true;
    }

differential equations: how to solve the natural frequency of the cantilever beam by mathematical method

I want to calculate the natural frequency of the cantilever beam according to the theoretical method.

enter the image description here

I find a post on how to solve the free vibration frequency of a cantilever beam with the finite element method.

(*https://mathematica.stackexchange.com/questions/99724/finite-
element-boundary-breaking*)
ps = {Inactive(
      Div)({{0, -((Y*ν)/(1 - ν^2))}, {-(Y*(1 - ν))/(2*(1 
- ν^2)), 0}}.Inactive(Grad)(v(x, y), {x, y}), {x, y}) + 
    Inactive(
      Div)({{-(Y/(1 - ν^2)), 
        0}, {0, -(Y*(1 - ν))/(2*(1 - ν^2))}}.Inactive(Grad)(
       u(x, y), {x, y}), {x, y}), 
   Inactive(
      Div)({{0, -(Y*(1 - ν))/(2*(1 - ν^2))}, {-((Y*ν)/(1 
- ν^2)), 0}}.Inactive(Grad)(u(x, y), {x, y}), {x, y}) + 
    Inactive(
      Div)({{-(Y*(1 - ν))/(2*(1 - ν^2)), 
        0}, {0, -(Y/(1 - ν^2))}}.Inactive(Grad)(
       v(x, y), {x, y}), {x, y})} /. {Y -> 10^3, ν -> 33/100}

{vals, funs} = 
 NDEigensystem({ps}, {u, v}, {x, y} ∈ 
   Rectangle({0, 0}, {5, 0.25}), 8)
theory = {0, 0, 0, 22/L^2 Sqrt((Y d^2)/(12 1)), 
   61.7/L^2 Sqrt((Y d^2)/(12 1)), 121/L^2 Sqrt((Y d^2)/(12 1)), 
   200/L^2 Sqrt((Y d^2)/(12 1)), π/L Sqrt(Y/1.)} /. {Y -> 10^3, 
   d -> 0.25, L -> 5}
TableForm(Transpose({Sqrt(Abs(vals)), theory}), 
 TableHeadings -> {Automatic, {"Calculated", "Theory"}})
bcs = DirichletCondition({u(x, y) == 0, v(x, y) == 0}, x == 0);

{vals, funs} = 
  NDEigensystem({ps, bcs}, {u, v}, {x, y} ∈ 
    Rectangle({0, 0}, {5, 0.25}), 5);
theory = {3.52 Sqrt((Y d^2)/(12 L^4)), 22 Sqrt((Y d^2)/(12 L^4)), 
    61.7 Sqrt((Y d^2)/(12 L^4)), π/2 Sqrt(Y/L^2), 
    121 Sqrt((Y d^2)/(12 L^4))} /. {Y -> 10^3, d -> 0.25, L -> 5.};
TableForm(Transpose({Sqrt(Abs(vals)), theory}), 
 TableHeadings -> {Automatic, {"Calculated", "Theory"}})
Needs("NDSolve`FEM`")
mesh = funs((1, 1))("ElementMesh");
Column(Table(uif = funs((n, 1));
  vif = funs((n, 2));
  dmesh = 
   ElementMeshDeformation(mesh, {uif, vif}, "ScalingFactor" -> 0.1);
  Show({mesh("Wireframe"), 
    dmesh("Wireframe"(
      "ElementMeshDirective" -> 
       Directive(EdgeForm(Red), FaceForm())))}), {n, 5}))

But I would like to know how to solve the natural frequency of the model in the previous post according to the partial differential equation solving method.

enter the image description here

Other related links:

How do you find the eigenvalues ​​of a PDE (Euler-Bernoulli dynamic beam)?

Euler-Bernoulli non-homogeneous dynamic beam equation with discontinuous parameters

Analytical solution of the Euler-Bernoulli dynamic beam equation with compatibility condition