spherical coordinates – construction of a purely radial harmonic function

So my question is

In a spherical shell with $ 1 <r <2 $ construct a purely radial harmonic function v so that it takes on the values $ 5 $ and $ 4 $ at the $ r = 1 $ and $ r = 2 $ , respectively

I know that I should use the Laplace sphere coordinates

and take $ Δv = 0 $

The spherical coordinates

$$ Delta v = frac {1} {r ^ 2} frac { partial} { partial r} left (r ^ 2 frac { partial v} { partial r} right) + frac {1} {r ^ 2 sin ^ 2 psi} frac { partial ^ 2 v} { partial theta ^ 2} + frac {1} {r ^ 2 sin psi} frac { partial} { partial psi} left ( sin psi frac { partial v} { partial psi} right). $$

But not sure which derivative I should be equal to 0 and then solve with a general solution

Can somebody help me with it

c ++ – Purely virtual function with different return types

I have a module with a parent class we call Parent and a number of children we call A, B, C. An external interrupt source triggers the receipt of a byte array, which is stored in a protected variable of the parent. My problem is that if the user wants to extract the data, it has to be converted into a user-friendly structure that is different for each of the children. I feel that in an OOP system, this data extraction function should be a purely virtual function declared by the parents and forcing their children to implement them because every child should implement this in this scheme. However, I'm not sure how to do this without making it complicated for the user (also known as void * for the return type) because each function returns a different data type. Below is an example of what my code would look like.

class Parent
{
    static void rxData(uint8_t* data, uint8_t ID)
    {
        //Copy data to the correct receiving Node using a hash of the ID
        memcpy(receivingNodesList(ID%3)->rxBuf, data, 20);
    }
    void setupReceive(void)
    {
        //Add this to the receivingNodesList
    }

    static Parent* receivingNodesList(3);
    uint8_t rxBuf(20);
}

class A final: public Parent
{
    //I feel like this should be an override somehow
    A_Data getRxData()
    {
        //Transform this->rxBuf into an A_Data object for return
    }
}

class B final: public Parent
{
    //I feel like this should be an override somehow
    B_Data getRxData()
    {
        //Transform this->rxBuf into a B_Data object for return
    }
}

Above you can see that the subordinate classes have the function & # 39; getRxData () & # 39; don't have to implement. However, I want there to be a purely virtual function or something that I don't know of in the parent class that enforces. If anyone has any tips on how I would achieve this or how they would solve this problem in general, they would be very grateful!

To edit:
Here is a code that uses rxData as a comment.

//Background on data types
struct A_Data
{
    float  temp;
    float hum;
};
struct B_Data
{
    float distance;
    int RPM;
};

void main(void)
{
    A myA;
    B myB;
    while(1)
    {
        if(myA.dataValid())
            LCD.Display(myA.getRxData());
        if(myB.dataValid())
            LCD.Display(myB.getRxData());
    }
}
```

Probability Theory – A purely discontinuous process with jumps +1 is Poisson.

I read Bass's book about stochastic processes alone. I will discuss the following exercise in Chapter 17.

17.8 Accepted $ X_t $ is an increasing process with paths that are right-sided with left-bounds $ X_0 = 0 $ how., $ X $ is purely discontinuous and all jumps are of size $ + 1 $ just. Suppose that $ lim limits_ {t to infty} X_t = infty, $ how. Then prove that $ X_t $ is a Poisson process with time change.

This exercise causes me discomfort. Suppose I have a (deterministic) process that skips every integer, and the jump sizes are one. Then this process fulfills all the hypotheses in the question, but how can it be a Poisson process? Jumps in the Poisson process are completely unpredictable. I can not handle this problem.

I would be glad if someone can clarify the problem and explain to me what I miss.

How do I create a purely functional language?

I'd like to create a purely functional programming language like Haskell – purely functional, sluggish – with curry functions, user-defined data types, type classes, all the bells and whistles.

I do not really know how to do that. I could to be able to implement a regular functional language, only with numbers, functions and no data types / type classes / curry functions / etc.

Could someone please give me general information on how to do this in Python, or provide resources?

P.S. I tried to read Write a Haskell but apparently it's not finished.

Also, if you've declined this question, I'd like to know why.

Ag.algebraic geometry – Purely inseparable morphism characterization

I have a question about Exercise 5.3.9 from Liu's "Algebraic Geometry" (page 208):

Enter image description here

Unfortunately, I have no idea how to (a) close the part

$ K (Y) to K (X) $ pure inseparable implies $ f $ purely inseparable.

By definition $ f: X to Y $ is called purely inseparable if $ f $ injective and if for everyone $ x ∈ X $, the extension of residual fields $ k (f (x)) → k (x) $
is a purely inseparable extension.

My thoughts:

We assume that $ K (X) / K (Y) $ is a finite pure inseparable extension.

Using the property of morphisms of annular spaces I get the following diagram

$$
require {AMScd}
begin {CD}
O_ {Y, f (x)} @> {} >> O_ {X, x} \
@VVV @VVV \
K (Y) = O_ {Y, eta_Y} @> {} >> K (X) = O_ {X, eta_X}
end {CD}
$$

By finiteness & pure separateness of field extension $ K (X) / K (Y) $ we obtain $ K (X) = K (Y)[a^{1/n}]$ for appropriate $ a in K (Y) $, The question is how this structure can be "translated" $ O_ {Y, f (x)} / m_ {f (x)} = k (f (x)) to k (x) = O_ {X, x} / m_x $?

On the other hand, there is another characterization of pure inseparable morphisms that applies to each area $ K $ the induced card $ X (K) to Y (K) $ is injective (see EGA 1 or Lius Ex. 3.8 from the previous page). But this approach does not help me either.

Does anyone know how I can attack the problem?

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& # 39);
var sidebar_align = & right; & # 39 ;;
var content_container_margin = parseInt (& # 39; 350px & # 39;);
var sidebar_width = parseInt (& # 39; 330px & # 39;);
// ->

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