## The derivation of the product in Sobolev SpPace

Let $$f in W^{1,infty}(0,T)$$
and $$g in W^{1,1}(0,T)$$ $$(0.

Is $$(fg)’= f’g+fg’$$ true.

Thanks

## Magento 2.3.6 Add Custom Sort For Product Graphql

I want to sort the products graphql with backorder and is_in_stock attribute. Please let me know if anyone has any solution for it.
I tried with quantity_and_stock_status it is applied only on qty.

## Why wont the product description attribute, when set to TextArea, convert line breaks to

Magento v2.4.2

My product description attribute was set to TextArea, and its worked fine for the last year. New lines where rendered as
in HTML on the product page. I decided to change it to TextEditor so I can use HTML. I didnt realize when I did that, all my non HTML descriptions would lose all their formatting and new lines or line breaks would no longer render as
and my descriptions would look like one giant run on paragraph.

So I changed the attribute back to TextArea thinking it would revert back. It didnt. There is still new line or line breaks in all the product descriptions, so the data is still here. Its just not rendering like it used to.

I have cleared the cache, redeployed etc etc…any ideas?

## Product are not displaying on Category page

main.CRITICAL: {"error":{"root_cause":[{"type":"illegal_argument_exception","reason":"Text fields are not optimised for operations that require per-document field data like aggregations and sorting, so these operations are disabled by default. Please use a keyword field instead. Alternatively, set fielddata=true on [shape] in order to load field data by uninverting the inverted index. Note that this can use significant memory."}],"type":"search_phase_execution_exception","reason":"all shards

## Product of Consecutive integers problem

I’ve begun pondering the following problem, and have found myself unable to advance on it; it goes like this:

Prove that the product of three consecutive integers is never the product of two consecutive integers (with a finite number of exceptions).

Now, I basically have very little idea of what to work with. Obviously, I have two exceptions: {1, 2, 3} ($$1 times 2 times 3 = 2 times 3$$) and {5, 6, 7} ($$5 times 6 times 7 = 14 times 15$$).

I formed the following equations:

$$x(x-1)(x+1) = y(y+1)$$

==> $$x^3 – x = y^2 + y$$

But I have no idea where to go from here. Graphing this on desmos yields the following elliptical curve, which I don’t think helps me:

Desmos graph

How do I prove/ this conjecture?

## pr.probability – All possible discrete probability distributions arising from a finite length product of stochastic matrices

Consider a discrete probability distribution $$x = (x_1,ldots,x_n)$$, where $$x_ige0$$, $$sum_ix_i=1$$, and a set of $$M$$ stochastic matrices $$P^1,ldots,P^Minmathbb{R}^{ntimes n}$$, where all $$P_{ij}ge0$$, and $$sum_{j=1}^nP_{ij}^m=1$$ for each row $$i=1,ldots,n$$ and each matrix $$m=1,ldots,M$$. Define $$mathcal{P}$$ to be the convex hull of the set of matrices $$P^1,ldots,P^M$$.

Now consider a positive integer $$z$$. I am interested in characterizing the set $$mathcal{Y}$$ of discrete probability distributions that arise from multiplying $$x$$ by all possible sequences of length $$z$$ of elements from $$mathcal{P}$$ (note that elements of $$mathcal{P}$$ are also stochastic matrices). That is, define

$$mathcal{Y}= {y=(y_1,ldots,y_n)mid y = xQ^{(1)}cdots Q^{(z)}, Q^{(j)}inmathcal{P},j=1,ldots,z}.$$

Is it possible to characterize $$mathcal{Y}$$ in terms of $$x$$, $$z$$, and some properties of the set of matrices $$mathcal{P}$$, e.g., their eigenvalues/eigenvectors?

## Vimeo video cannot insert in product page

I am trying to add Vimeo video on product page, but having error that saying video not found.
I did check the video setting, it is fine and open to public. Anyone know why?

## Woocommerce Custom product fields need to be editable after purchase in View Orders Page

I want to display that checkout custom fields on My Account > View Order Pages, to allow customer to edit its value after purchase, so Customers can change and save the custom field value.

Any help?

## performance tuning – Fast Evaluation of a series of dot product

Context

I have a function that depends on 3 real variables x,y and z and that is defined by a series of matrix products. The evaluation of f for a specific (x,y,z) is fast ~0.02 sec but I want to evaluate the function on a huge number of points (a regularly spaced grid of x,y and z values) which in the end makes the evaluation really slow if not unmanageable. I have already tried what was proposed in this answer, but my function is not compilable, and ParalellTable is faster that vectorizing on my laptop.

Illustration

For the sake of simplicity let me illustrate this with

``````weight = RandomReal(1, 200);
pts = RandomReal(1, 200);
M = RandomReal(1, {200, 200});
f(x_,y_) = (weight*Exp(-pts*x)).Exp(M).(weight*Exp(-pts*y))//N
``````

How would one make the evaluation of f on multiple couples of (x,y) faster than relying on ParallelTable ?

``````ans = ParallelTable(f(x,y),{x,Range(100)},{y,Range(100)})
``````

Thanks a lot for your help!

## magento2.4 – Product Qty instead Salable Qty

How can i call Product Qty instead Salable Qty in

``````            if(\$product->getTypeId() == 'simple') {
\$objectManager = MagentoFrameworkAppObjectManager::getInstance();