Zero Of A Function Puns

I see people doing stuff like

class StateBase {
  public:
    StateBase(Application &app)
        : m_pApplication(&app)
    {
    }

    virtual ~StateBase() = default;

    virtual void foo(Event e) = 0;
    virtual void bar() = 0;
   
  protected:
    Application *m_pApplication;
};

And then

class StateDerived: public StateBase {
  public:
    StateDerived(Application &app);

    void foo(Event e) override;
    void bar() override;

//...
};

Is this somehow equivalent to default initialization? Does it set void to a null pointer? This code snippet is particularly cryptic to me, not sure what it aims to achieve.

Taking the Calc AB test tomorrow and have a Ti-84 there has to be an easier way than graphing to find x intercepts

I was reading transfer function and how to find the number of infinite zeros. Is it possible that given a generic system = G(s), where G(s) = N(s)/D(s). What is the advantage or disadvantage of having a large number of infinite zeros? Also is it possible to have number of zeros greater than the number poles in system G(s)?

Just got to the chapter "Identifying Roots and Zeros of a Polynomial Function" and I'm getting pretty confused at one part. Heres a picture of the intro to the lesson https://imgur.com/a/9bhtl. The part that is confusing me the most is in the 4th paragraph.

Two of the questions to practice this is:

i) y=(x–1)^2 (x+3)

• When I first look at this I can state the x-intercepts. Being 1 and -3. So if I understand this correctly y= (x-1)^2(x+3) = 0 has a double root (order 2) at x = 1 and a single root of (order 1) at x = -3.

ii) y=(x–1)^3

• When I look at this I can see one x-intercept that being 1. So does y=(x-1)^3 has a triple root (order 3) at x = 1.

The thing that gets me more confused is that it then asks for "What is the relationship between the number of x-intercepts on the graph and the order of the zeros in the equation of the function?" I didn't know the answer so I looked at the given answer for this question and it was "The number of x-intercepts corresponds to the number of distinct zeros no matter what order each has." I have no idea what this means, the only guess I have is that for example question ii) it has a order of 3 but only has one x-intercept so how does the x-intercepts corresponds to the number of distinct zeros.

Hi, I am estimating the parameters of a system which is linear. I have differential equations for the system but I discretize them so at the end I can represent the system such as:

U = A*p

where U is something I can measure, A is a matrix which coefficients I know and p are the unknown parameters.

Let length(U) <= length(p)

Then I hypotize that an optimization method that goes contrary to the gradient scaled will always converge to the true values of the system (p) as long as the magnitude of the changes in each iteration is small enough, independent of the starting points or cost functions used and also assuming I randomize the measurements so U and A change all the time.

I have proved this for different cost functions using the sum of the absolute errors and the sum of squares. I tried with different exponents in the cost functions such as sum((U'-U)^(2*n)) and the hypothesis always holded true as the gradient only became zero when the fit was perfect or in certain combinations of U and A and hence the added "and the variables that affect the system randomized".

I was curious if maybe this can be generalized for any cost function used. Maybe it can be easily proved playing a bit with the chain rule but I'm curious if something like this has been proved before.

3...2...1... FIGHT!!

Hello everyone. I try to plot a figure of a journal article. I gave the equations, the expected figure and my incorrect figure in the attached image file. I wrote a code for that:

phi = linspace(0.001, 1000, 1000000);
v = 2;
lRp = sqrt((1./phi).*((v+1)^2-1));
I1 = besselj(1,lRp);
I0 = besselj(0,lRp);
h = 1 - 2./lRp*(I1/I0);
plot(phi,h)
set(gca, 'XScale', 'log')

But it doesn't work as expected. I obtain the figure on the right, given in the attached image file. May you help me to find my error? Thanks a lot!

https://preview.redd.it/o5h4c6bmnav41.png?width=1078&format=png&auto=webp&s=50a70f5b667eb0675f49ea51d875e779d849db78

Hi there,

I'm trying to draw a Bode plot for the transfer function (-8.1899*10^(-3) * s) / (8.4732 * 10^(-4) * s + 1) .

I'm having the worst time trying to figure this out. How do I draw a Bode plot for a transfer function with a zero at zero? All the resources I can find online only give instructions for nonzero zeros. Also, how does the coefficient -8.1899*10^(-3) play into it? Does it even matter?

Thank you for your help.

I tried to calculate zeta of -2 but I got something which is not zero (1/96) and I can't seem to find why or how it could be zero. Any kind of help is welcome.

bruh why do i have to do all of this. goddamn this is like school, so organized but unnecessary. so all I get is that x + y = some number, and x + y straight up can be anything.

so like this if i make a chart.

x y

1 100

2 69

3 21

so there, it's not a linear function cause the y doesnt make sense at all. its clearly not a same - for both, like im too lazy to calculate. ok fine its -31 then -48, so its not right. or do i not get what linear function means?

Hi, I'm looking at the solution to one of the homework problems, and I saw this.

https://i.imgur.com/HLbINkp.png

If we want to boost the magnitude of the frequency response to 0dB, why do they add a pole (s+a)? I thought we would need to add zeros in the transfer function's numerator since we already have two poles that would make the system -40dB. I'm so confused right now. Thanks.

I read when it was done in Japan in the 90s it led to reduced spending and more hoarding which led to reduced demand and layoffs.

But what I don't understand is how is that different than now? Too much inflation and everything is very hard to afford so those that can hoard still do and companies still layoff due to other factors.

Can marketing help an economy performing zero inflation or deflation?

ELI5 OR ELI16 as much as possible. I'd like to know if there are people with theories on how to reduce inflation. Because as far as I know, nothing can keep growing forever.

For some context I'm subtracting the sums of two different ends of a table with =SUM(B22:H22) - SUM(I22:J22) - K22. It works, but my answers which should be coming out as zeros(For accounting purposes) appear as dashes. Please and thank you.

Hi. In my smooth manifolds class, I believe the proffesor told me that a k codimensional submanifold will be the zero set of k functions if and only if the normal bundle is trivial. I wanted to make sure that I am remembering this correctly. I have been able to sketch a proof for the (zero set of functions implies trivial normal bundle) direction, involving Riemannian metrics (which I do not know a lot about), but have not made any way on the other direction, so I wanted to make sure I am not forgetting any hypothesises. Also, I am interested in weather or not something like this can be true in Algebraic Geometry. I am skeptical that it can be exactly the same, as every closed variety in an affine variety is the zero set of some functions, and practically no sub variety is the zero set of some functions for projective varieties.

Are they all essentially the same on the I side? My electrical knowledge consists of turning the lights on and off - but if someone could help me identify a piece that needs to be reconnected? Swap out a battery? String some tinfoil across to a new battery?

I’ve been cleaning house and found lots of these old cards, my 4yo loves them but most don’t work.

Say we have the function y=x^2 -x-12

Could someone please explain I cannot find anything by googling

If critical zeros are in the critical strip 0 < Re(s) < 1, then what do you call zeros on the critical line Re(s) = 1/2? Supercritical?

What are the hypothetical non-trivial critical zeros off the critical line?

Why is it that when an enzyme gets too hot, even though it's supposed to denature, its efficiency just goes down a little before really taking a dip? What is going on during that little temperature range where the efficiency slowly goes down but doesn't plummet if it is supposed to be being denatured?

Hey! Can someone help me find the zeros to this equation algebraically? I used desmos to graph it and I got the zeros of x=1 and x=4 but I don't seem to be getting that result when I try to solve for x algebraically.

:9\left(\frac{\left(x-4\right)^3}{2.718}\right)+9x\left(\frac{3\left(x-4\right)^2}{2.718}\right) (if you wanted to graph it, it might work on desmos)

The function: f(x) = 9[(x-4)^(3) / 2.718] + 9x[3(x-4)^(2) / 2.718]

Thank you!

I have an array of names sorted in descending order by popularity, from John (at index 0) on down to Broderick (at index 1218). I need to choose one of the names randomly, but I want the more common names returned more often. So basically I need a function that returns numbers on a half-bell curve with lower numbers more often and higher numbers less often.

 Dim names As String() = My.Resources.mnames.Split(vbCrLf)
 Dim x As integer
 Dim pick As String
 
 x = RandomHalfBell(UBound(names))
 pick = names(x)

Something like that. So what does the RandomHalfBell function look like?