gamma function – Maximum likelihood estimator for 2 different samples

How to derive maximum likelihood estimator for /omega given by ml omega given 2 random samples (X1,Y1),……,(Xn,Yn). Where X is pulled from the gamma distribution and the Y comes from the standard normal distribution. The gamma distribution has a known shape variable = 3. How do you derive the maximum likelihood estimator for omega?

web part – SPFX JSOM – call a named function from executeQueryAsync

Apologies in advance for the newbie question as I believe this is actually a fairly simple issue. I am using JSOM and in my WebBart.ts file have a named function that queries a list and produces front-end output. It works without issues:

      private PopulateExistingVacancies(): void {

In a different function (triggered via an event listener), I do an asynchronous call:

    protected FinalizeVacancy(): void {


                // Execute the asynchronous operation and on success update status 
                // and attempt to run additional (pre-defined logic) 
                context.executeQueryAsync(function () {
                    (<HTMLDivElement>(document.getElementById("lblMsgInfo"))).innerText = "New Vacancy entry has been created";
                  function (sender, args) {
                    (<HTMLDivElement>(document.getElementById("lblMsgError"))).innerText =
                      "Error encountered adding new Vacancy entry: " + args.get_message();

On success, I would like to actually call PopulateExistingVacancies(), but I don’t think this is possible (or at least it won’t work).

So my question is, what is the proper way to call a pre-written function from an anonymous function which is executed upon an asynchronous success?

Thanks in advance.

Show that a function f, continuous on (a,b), has an abs minimum value. The limits as x approaches either bounds of the interval is +Infinity

Can you show that the function f must have an absolute minimum value on the interval (a,b), if f is continuous on (a,b) and the right hand limit as x->a along with the left hand limit as x-> b are both equal to positive infinity?

javascript – $(…).summernote is not a function

I have the Summernote editor on a couple of pages of my site.
On one page I’m not getting this error, but the other throws this exception:

TypeError: $(...).summernote is not a function update:110:30
    jQuery 2

JQuery is being loaded on both pages.
I checked Summernote for notes about compatibility with the version of jQuery I’m using, and there’s not any issue there.
I tried putting “defer” in the Summernote script load to no avail.
Any ideas you have regarding why this would be working on one page, but not the other are very welcome.

Here’s the relevant part of the page:

    <form method="post">
      <div class='form-group'>

        <label for='summernote'>Content</label>
        <textarea id="summernote" name="about" class='form-control'></textarea>
        <script type="text/javascript">
        $(document).ready(function() {
              placeholder: 'Enter some content here.',
              tabsize: 2,
              height: 200,
              fontNames: ('Arial', 'Impact', 'Tahoma', 'Verdana', 'Roboto'),
              fontNamesIgnoreCheck: ('Arial', 'Impact', 'Tahoma', 'Verdana', 'Roboto'),
                ('style', ('style')),
                ('font', ('bold', 'underline', 'clear')),
                ('fontname', ('fontname')),
                ('color', ('color')),
                ('para', ('ul', 'ol', 'paragraph')),
                ('table', ('table')),
                ('insert', ('link', 'picture', 'video')),
                ('view', ('fullscreen', 'codeview', 'help')),
                ('highlight', ('highlight')),
      <div class='form-group'>

algebraic curves – Under what conditions is the compositum of two rational cubic Kummer extensions a rational function field?

Let $k$ be an algebraically closed field of characteristic $p > 3$ and $F = k(x)$ be the rational function field in the variable $x$. Consider two Kummer extensions $F_1 = F(sqrt(3){g_1})$, $F_2 = F(sqrt(3){g_2})$ of degree $3$, where $g_1, g_2 in F^*$. Suppose that $F_1, F_2$ are also rational, that is $F_1 = k(x_1)$, $F_2 = k(x_2)$ for some $x_1 in F_1$, $x_2 in F_2$.

Under what conditions is the compositum $F_1F_2 = k(sqrt(3){g_1}, sqrt(3){g_2})$ a rational function field?

wp_redirect function is not working

I am using this code to redirect.

Note: I am using these lines of codes in the template file.

$url = ‘’;


What should I use to do it to make it happen?

navigation – How do you pick the right function to be in the bottom menu?

Im currently designing a student portal mobile application.
It got a lot of functions; 1. frequently used (academic, timetable, assignments) 2. seldom used (fees, library) and 3. others that are not applicable to all students (counselling, international students, visa).

I could not figure out the categorisation of functions and where they should belong.

  1. I plan to have the bottom menu for management (dashboard, timetable, fees, notification, menu).
  2. Then, maybe have shortcut buttons in dashboard for academic, library, hostel. This shortcut is for big functions that have have a lot of features and integration in the future. Example in library, user can search for books, reserve and pay fines.
  3. And the less important ones to be placed in menu (menu in bottom navigation > sidebar).

Or would you guys suggest functions to be categorised based on usage frequency? or maybe theres other factors to be considered?

I really appreciate your help. Thank you in advance!

Asymptotic behavior of maximum of bessel function

Let $J_n$ be the Bessel function of the first kind. Let $J_n^{(max)} = max_{x>0} J_n(x)$. What is known about the asymptotic behavior of $J_n^{(max)}$ at large $n$? Specifically, I am looking for a lower bound. It is ok if the result only holds for integer and half-integer $n$.

(It is potentially helpful to note that $J_n^{(max)} = J_n(j’_n)$ where $j’_n$ is the smallest positive zero of $J’_n$, i.e. the global maximum of $J_n$ occurs at the “first” local maximum.)

nonlinear optimization – Gradient of the function in the BFGS Quasi-Newton Algorithm

I have a function $f=sumlimits_{k=1}^{K}|R_{k}^{dl}- R_{k}^{ul}|$ that I want to minimize using the BFGS Quasi-Newton algorithm.

If $R_{k}^{dl} = y_k times A times B times C$.

$y_k$ and $R_k^{ul}~ forall~ k in {1, 2, dots, K}$ are given.

Also, $A$ is given, $B$ is not given, and $C$ is a function of $B$ only.

If I want to calculate to the gradient of the function ($nabla f$). Should I calculate it with respect to all variables or with respect to $B$ only?

Proof there exists M ∈ ℝ s.t f(x) ≥ M when lim f(x) = 1 and f is a continuous function

I need help deriving a proof to show that given,

f: (0,∞) → ℝ is a continuous function and lim(x→∞) f(x) = 1

that there exists an M ∈ ℝ such that, for all x ≥ 0, we have f(x) ≤ M.