i had upgraded magento 1.9 to magento 2.4 but it did not work properly so i decided to get back but when i restored it i can see this problem

error log
[14-Apr-2021 15:18:01 Australia/Sydney] PHP Fatal error: Uncaught Error: Class ‘MagentoFrameworkAppErrorHandler’ not found in /home/martarab/public_html/bin/magento:20
Stack trace:
#0 {main}
thrown in /home/martarab/public_html/bin/magento on line 20
enter image description here

sequences and series – New chess grains problem

The original chess grains math problem stablished that on the first square of the chess board you put a rice grain, on the second you put two, the third four and so on, everytime having in the next square available the double from the last one. Now my question is how to calculate the rice on any square and on the entire board if instead of doubling the quantity of the last one, you multiply it by itself (except for the fisrt square of course, that would be too easy). In the first you will have one, in the second 2, in the third you have 4 and in the fourth 16, then 256, 65536, and so on.

Shannon information problem

Given a discrete distribution $P(X_1,X_2)$, is it possible to build $P(X_1,X_2,Y)$ such that
I(X_1;X_2) = I(Y;X_1,X_2)

where $I$ is Shannon’s mutual information?

Data files half empty in SQL Server. Is that a problem?

I have a multiple TB database and I have been doing some clean-up and dropped many tables. So now the data files are half empty. If I don’t care about releasing the space to the operating system, is there any other reason to shrink the files?
I am thinking that now at least I do not need to worry about auto-growth settings, which might slow things down if I add a large table with ETL.

algorithms – How to prove that one problem belongs to class P?

Is there any typical proving method when proving that one problem belongs to class P?

For example, when proving that

The problem of finding n to the kth power is the P problem. (Each multiplication can be done in unit time)

If you present an algorithm that can solve this problem with $O (log n)$, can it be a proof?

Help with a geometry problem with a triangle and its orthocentre

Let ABC a traingle inscribed in a circle with radius 1 and center O. Let the angle AOM=150 where M is the middle BC. Let H the orthocentre of the triangle. If A,B,C are selected such that Oh has the minimum lenght, than the lenght of BC is
A: $sqrt{15}$
B: $sqrt{13}/2$
C: $sqrt{3}/2$
I made a sketch and tried to apply the Sylvester’s theoreme and to solve the problem with vectors but did not succed. Could you please help me?

WordPress warning problem

Warning: Declaration of ET_Theme_Builder_Woocommerce_Product_Variable_Placeholder::get_available_variations() should be compatible with WC_Product_Variable::get_available_variations($return = ‘array’) in /homepages/0/d786463972/htdocs/clickandbuilds/test/wp-content/themes/Divi/includes/builder/frontend-builder/theme-builder/WoocommerceProductVariablePlaceholder.php on lineenter image description here

st.statistics – Binary Regression : Is this an open problem in Mathematics/Statistics?

Let $X$ be a random variable which takes values from $Omega = (0,1)^m$ with a probability distribution $p(x)$. Assume $p$ is a BV function with non zero total variation and $p(x)>0forall xinOmega$. There is a discrete random variable $Y$ which takes values from ${0,1}$ and depends on $X$ with $P(Y=1/X=x) = eta(x)$. Assume that $eta$ is also a BV function with non zero total variation and no removable discontinuities.

Binary Regression Problem

Given no other information except $n$ samples of the random variable pair $(X,Y)$ drawn iid, that is $(x_1,y_1),(x_2,y_2),ldots(x_n,y_n)$ one need to give a method for computing $tilde{eta}_n$, an estimate of $eta$ such that $$limlimits_{ntoinfty}|tilde{eta}_n-eta|_{L^2(Omega)} = 0$$

This problem I believe is open (needs confirmation as I have little knowledge on statistics literature). There are methods like $k$-nearest neighbours method, which solves when $eta$ belongs to a narrower class of absolutely continuous functions. There seem to be some methods when $eta$ is a Lipschitz continous function, but with known Lipschitz constant.

For $eta$ belongs to class of all BV functions with nonzero total variation (a wider class), I believe I have come up with a method and proof of convergence. Is this sufficiently interesting to be considered for a mathematics journal or it should be considered for a (mathematical)statistics journal? How interesting is this problem for mathematicians and/or statisticians?

magento2 – i had newly installed the magento 2 and this problem is occuring with elasticsearch please help

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