I do the settings to show price include Tax in Configuration > Settings > Stores > Sales > Tax > Price Display Settings > Display Product Prices In Catalog and Display Shipping Prices. Configuration > Settings > Stores > Sales > Tax > Shopping Cart Display Settings > Display Prices and Display Subtotal. On product […]

I want to add some custom content under the shopping button on the product page of the specified category. I have used the block and widget functions to create it, but the display position is not what I want. How to achieve it?

I have a bunch of ordered pairs x, y where 0 < x < y <= n (some given upper bound) like S = [(1,2), (1,3), (1,4), (2,3), (3,4)] I need to find the Length of the longest subset where all the numbers within the ordered pairs are unique. Here that would be 2. eg: […]

## Lévy Khinchine Proof

I am supposed to prove this theorem Theorem 1.16 For a semimartingale levy process X, there is a continuous non decreasing function $\beta$ with $\beta_0 = 0$, a measure $\kappa$ satisfying the conditions of the theorem 1.11 such that : $\mathbb{E}[e^{iu(X_t-X_0)}] = \exp\{iu\alpha_t – \frac{u^2}{2}\beta_t + \int_{]0,t] \times \mathbb{R}} (e^{iux} – 1 – iux 1_{|x|\leq1} […]

Find all polynomials P(x) with real coefficients such that $(x-8).P(2x)=8(x-1).P(x).$ Find all polynomial $P(x)$ with real coefficients such that $(x^2 -ax + 18).P(x) = (x^2+3x).P(x-3).$ In second one,I plugged, $x=-3,$ then, a=-9 further it simplifies to:$(x+6).P(x)=(x).P(x-3)$. putting $x=-6,$ $P(-9)=0$ putting$ x=0,$ $P(0)=0$ So, $P(x)=x(x+9).Q(x)$ putting the above value of $P(x)$, $(x+6)(x)(x+9)Q(x)=(x)(x-3)(x+6)Q(x-3)$ $(x+9)Q(x)=(x+6)Q(x-3)$ Now, here I […]

In my real analysis textbook, they present the proof of L’Hopital’s by using Cauchy’s mean value theorem. The part in the proof I am struggling to work out rigorously is a particular implication involving equivalent limits using different variables. We have assumed that $f(c)=g(c)=0$, $f$ and $g$ are differentiable on a neighbourhood of $c$, and […]

For a unital ring $R$, there is a homomorphism $f:\mathbb{Z}\rightarrow R$ and the kernel is an ideal of the form $n\mathbb{Z}$ for unique $n\in \mathbb{N}$ which we call the characteristic of the ring. In a similar kind of way, for a group $G$, and $g\in G$ there is a homomorphism $f:\mathbb{Z}\rightarrow G$ sending $n$ to […]

I’m reading Wagon’s book “The Banach-Tarski paradox”. At page $149$, the author talks about the “direct union of a directed system of amenabile groups” without defining it. Q1: does direct union simply mean union? If this is the case, why does he use the adjective “direct”? Or is direct union the same as direct limit? […]

Bayesian Network I am working on an exercise that find out certain probability based on a Bayesian Network. The Bayesian Networking showed on the above The following are my work out: P(C ∩ S ∩ E ∩ ¬P ∩ ¬F) = P(¬F | C ∩ S ∩ E ∩ ¬P) ⋅ P(C ∩ S ∩ […]

Prove that $H_1/N∩H_2/N≌(H_1∩H_2)/N$ I have no idea how to solve this problem.Is there anyone help me?