All Questions

I think I found a proof, that on Lipschitz domains $\Omega$, $H^{1+s}(\Omega)$ is the dual space of $H^{1-s}(\Omega)$ with respect to the $H^1(\Omega)$ scalar product for all $0\leq s<1/2$. Does ...

Is there some kind of classification of affine spaces such that every homotopy group of the space has no torsion? Any reference on this topic will be most welcome.

In a paper about Presburger Arithmetic, Lukasiewicz's axioms of propositional calculus are written as follows: CCpqCCqrCpr CCNppp CpCNpq I am having a hard time understanding what these axioms ...

A weakly nonlocal second order elliptic PDE is one which can be expressed in the form $$F(x,u,Du(x),D^2u(x))=0$$ where $F(\cdot,\cdot,\cdot,X) \leq F(\cdot,\cdot,\cdot,Y)$ whenever $Y \preceq X$. ...

Consider a (closed) Riemann surface and let $G(x,y)$ be the Green function of the Laplace-Beltrami operator. We can informally identify $G$ with the two-point correlation function for the Gaussian ...

In a paper by Roitman there is the following argument in the proof of the Proposition 3.4: Let $f:A\to B$ an epimorphism of abelian varieties. By the complete reducibility theorem (see Mumford´s ...

Let $G$ be a compact, connected Lie group. There is an Atiyah–Hirzebruch spectral sequence $$H^*(BG;K^*) \implies K^*(BG)$$ connecting $H^*BG$, which generally contains torsion, with $K^*BG \cong \...

We know that given a finite group $G$ and its group 4-cohomology class $w \in H^4[G;U(1)]$, we can obtain a DW topological invariant $Z_{G,w}(M^4)$ as the partition function of the DW theory on a ...

Please I find it quite different to evaluate the terms Ao and Bo from these expressions and before then I need to evaluate P2m and Q2m.how do I figure out these four quantities on the screen shots ...

I have a question about some notation in the book "Semiclassical Analysis": What worries me is the interpretation of the derivative $D_{x_j}$ in the third and second-to last equation. The author ...

Consider a function $f:\mathbb{R}^{2\times 2} \rightarrow \mathbb{R}^{2\times 2}$. $f$ convex is characterised by the sign of the eigenvalues of the Hessian matrix of $f$. Is there a similar ...

Let $n \ge 2$. Set $\dot{H}^1(\mathbb{R}^n)$ to be the homogeneous Sobolev space, defined as the Hilbert completion of $C_0^\infty(\mathbb{R}^n)$ with respect to the norm $\| \varphi \|^2_{\dot{H}^1} \...

Let $A_n$ be the matrix product of $n$ i.i.d. N-by-N random complex matrices. The matrix distribution is not fixed and can be tuned to suit specific solution if needed, as long as it's not too "...

Is there any homeomorhpism from $\mathbb R^n$ to $\mathbb R^n$ that transforms an ellipsoid of the form $\{x|x^T A x\leq 1\}$ (=ellipsoid centered at the origin) into a hyperrectangle, and transforms ...

I have trouble to find references on the use of energy method (Faedo-Galerkin method using approximation in finite dimension space) to solve problems of the form $$ \begin{cases} \partial_t u = \...