MathOverflow

Let $P_t(x) = \frac{1}{\sqrt{4\pi t}} e^{-\frac{x^2}{4t}}$ be the heat kernel on $\mathbb{R}$. Consider the operator $C_\epsilon$ defined by:$$C_\epsilon((t_1,x_1),(t_2,x_2)) = \epsilon^{-2} \int_{|t_1-t_2|}^{t_1+t_2} \left( P_{s+2\epsilon}(x_1-x_2)...

Is simple intuitionistic type theory (Lambek, Scott "Introduction to higher order categorical logic") complete relative to
Grothendieck toposes
Heyting-valued sets

This problem is exercise 11 in Filippo Santamborgio's book, Optimal Transport for Applied Mathematicians.
Let $A$ and $B$ be two symmetric positive definite matrices, and let $L_A, L_B : \mathbb{R}^d \to \mathbb{R}^d$ be affine functions defined by:
$$L_A(x) = Ax + a, \quad L_B(x) = Bx + b$$...

Can you help me to find down the fundamental unit of the cubic below:x(x-3)(x-6)-1=0.I found that if \alpha is one of the roots then by calculating the regulator of \alpha and \alpha - 3, its satisfy the condition of corollary 5.9 of the paper : https...