Related papers: The kernel and the injectivity of the EPRL map
This is a light expository article. It explains a proof, due to Peter Doyle and Cecil Qiu, the following result from set theory. Let A and B be sets. Suppose there is an injective map from A x {0,...,n-1} into B x {0,...,n-1}. Then there is…
The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are provided. Numerical simulations are presented to illustrate…
Given an open, bounded, planar set $\Omega$, we consider its $p$-Cheeger sets and its isoperimetric sets. We study the set-valued map $\mathfrak{V}:[\frac12,+\infty)\rightarrow\mathcal{P}((0,|\Omega|])$ associating to each $p$ the set of…
A drawing in the plane ($\mathbb{R}^2$) of a graph $G=(V,E)$ equipped with a function $\gamma: V \rightarrow \mathbb{N}$ is \emph{$x$-bounded} if (i) $x(u) <x(v)$ whenever $\gamma(u)<\gamma(v)$ and (ii) $\gamma(u)\leq\gamma(w)\leq…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
It is well known that kernels in graphs are powerful and useful structures, for instance in the theory of games. However, a kernel does not always exist and Chv\'atal proved in 1973 that it is an NP-Complete problem to decide its existence.…
Fessler and Gutierrez \cite{Fe,Gu} proved that if a non-singular planar map has Jacobian matrix without eigenvalues in $(0,+\infty)$, then it is injective. We prove that the same holds replacing $(0,+\infty)$ with any unbounded curve…
Given a closed oriented surface $\Sigma$ of genus at least two, the Goldman trace map defines a function from the vector space generated by the free homotopy classes of oriented closed curves to the Poisson algebra of regular functions on…
In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $\Gamma$-ring satisfying the some conditions, then any $n$-multiplicative…
We show injectivity results for assembly maps using equivariant coarse homology theories with transfers. Our method is based on the descent principle and applies to a large class of linear groups or, more general, groups with finite…
We give an explicit integral formula for the Dunkl kernel associated to root system of type $A_2$ and parameter $k>0$, by exploiting recent result in [1].
The kernel of a pair of linear systems is studied in the framework of commutative ring theory with applications to behavioral perspective of linear systems
The recently discovered correlation between the rest frame GRB peak spectral energy $E_{\rm peak}$ and the collimation corrected energy $E_\gamma$ in long GRBs is potentially very important, yet awaits confirmation from an independent…
Let $R$ be a ring (associative, with 1), and let $R<< a,b>>$ denote the power-series $R$-ring in two non-commuting, $R$-centralizing variables, $a$ and $b$. Let $A$ be an $R$-subring of $R<< a>>$ and $B$ be an $R$-subring of $R<< b>>$, and…
We study the injectivity of the cycle class map with values in Jannsen's continuous \'etale cohomology, by using refinements that go through \'etale motivic cohomology and the ``tame'' version of Jannsen's cohomology. In particular, we use…
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…
We investigate the geometry of smooth hyperelliptic curves that possess additional involutions, especially from the point of view of the Prym theory. Our main result is the injectivity of the Prym map for hyperelliptic…
A (possibly denerate) drawing of a graph $G$ in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph…
We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.