Most active questions
215 questions from the last 7 days
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Generalization of Connes metric on state space
Let we have a spectral triples $(A,H,D)$
The Connes distance on the space of states of $A$ is the following:
$$d(\phi,\psi)=sup_{ |[D,a]|\leq 1} |\phi(a)-\psi(a)|\quad (*)$$
Is this metric ...
- 366
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What do we know about Poisson boundaries of arbitrary Riemannian manifolds?
For closed manifolds, we know that the Poisson boundary is trivial due to compactness and for radially symmetric manifolds for which diffusion is one dimensional, there are A Brief Introduction to ...
- 168
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References for Hilbert Space Structure and Density of Smooth Functions in Weighted Sobolev Spaces on $ \mathbb{R} $
I am looking for references and materials that discuss the following aspects of weighted Sobolev spaces $ W^{k,2}_\rho(\mathbb{R}) $ defined on the entire real line $ \mathbb{R} $:
Hilbert Space ...
- 131
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question about some algebraic simplifications performed as we solve differential equations with Laplace transform
I am trying to follow this discussion of Laplace transforms on youtube:
https://www.youtube.com/watch?v=ofvkZXgbIxE&t=610s
The relevant portion is 10 minutes in to the video.
There is some algebra ...
- 101
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Convergence of measures in the Lévy–Prokhorov metric and weak convergence of measures
How to prove that over R the convergence of measures in the Levi-Prokhorov metric is equivalent to the weak convergence of measures
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Explicit rate of decay of the positive standing wave of the subcritical nonlinear Schrödinger equation
Consider the following semilinear problem:
$$
\begin{cases}
- \Delta u + u = u |u|^{p - 2}
&\text{in} ~ \mathbb{R}^N;
\\
u (x) \to 0 &\text{as} ~ |x| \to \infty,
\end{cases}
$$
where $N \geq 2$...
- 144
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103
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On the form of algebraic numbers belonging to a specific field extension
Let $m>1$ be an integer and set $\theta=10^{-1/m}$. For a $\gamma\in \mathbb{Q}(\theta)$, there exists $a_0,\ldots,a_{m-1}\in \mathbb{Q}$ such that
$$
\gamma=a_0+a_1\theta+\cdots+a_{m-1}\theta^{m-1}...
- 515
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80
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The definition of Hodge bundles with metric
A system of Hodge bundles is a direct sum of holomorphic vector bundles $E = \oplus_{p+q=n} E^{p,q}$ with a morphism $\theta : E^{p,q} \rightarrow E^{p-1,q+1} \otimes \Omega_X^1$ such that $\theta^2 = ...
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What is a quantum condensed space?
Due to a categorical equivalence involving compact topological spaces and unital commutative $\mathrm{C}^*$-algebras, there is a practise involved in so-called quantum mathematics where a ...
- 1,037
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Why do we require that all successors model this formula?
I'm reading Fitting's Intuitionistic Logic, Model Theory and Forcing. This occurs in Chapter 7.15.
The aim is to prove that a certain intuitionistic model is an intuitionistic model of ZF. I ...
- 139
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3
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Is rank of the length spectrum of a closed negatively surface/manifold infinite?
Suppose that $(S,\mathfrak{g})$ is a closed negatively curved Riemannian surface =(or more generally a manifold). Negative curvature guarantees that the non-trivial conjugacy classes $\text{conj}(\...
- 89
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Chains with full range on a Boolean algebra with convex measure
Preliminaries. Let $X$ be a set and let $\mathcal A$ be a Boolean algebra of subsets of $X$ (i.e., $\mathcal A\subset 2^X$ such that $\mathcal A$ contains the empty set and is closed under finite ...
- 111
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Third order estimate for linear elliptic equations
Let $\lambda < A < \Lambda$ be a constant symmetric matrix and $u$ be a $C^{\infty}$(elliptic regularity gives smooth solutions) solution of $\text{div} A \nabla u = 0$. Let $S_1$ be a sphere ...
- 455
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49
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The relation between Hodge bundles with metric and polarized variation of Hodge structures
Recently I've been reading Simpson's paper "constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, 1988, JAMS". On page 898 he mentioned about ...
- 11
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Conditions on SDE coefficients for well-posedness of Fokker-Planck equation
Consider the following $n$-dimensional Ito-SDE:
\begin{align}
dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t
\end{align}
What are the necessary regularity conditions on $\mu$ and $\sigma$ to ensure that the ...
- 111