We prove a generalization of the Schwarz–Carathéodory reflection principle for analytic maps f from the unit disk into arbitrary Riemann surfaces equipped with a complete real analytic conformal Riemannian metric λ(w) |dw|. This yields a necessary and sufficient condition for f to have an analytic continuation in terms of the pullback of the metric λ(w) |dw| under the map f .

We present a simple categorical semantics for ML signatures, structures and functors. Our approach relies on realizablity semantics in the category of assemblies. Signatures and structures are modelled as objects in slices of the category of assemblies. Instantiation of signatures to structures and hence functor application is modelled by pullback.

Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusi...

To unravel the structure of fundamental examples studied in noncommutative topology, we prove that graph $C^$-algebra $C^(E)$ a trimmable $E$ is $U(1)$-equivariantly isomorphic to pullback subgraph $C^(E'')$ and functions on circle tensored with another $C^(E')$. This allows us approach K-theory fixed-point subalgebra $C^(E)^{U(1)}$ through (typically simpler) $C^$-algebras $C^(E')$, $C^(E'')^{...

We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot K in its m-fold cyclic branched cover Σm(K), and we give computations when m = 2 for over fifty three-bridge knots with up to eleven crossings.

Pullback rewriting has recently been introduced as a new and unifying paradigm for vertex rewriting in graphs. In this paper we show how to extend it to describe in a uniform way more rewriting mechanisms such as node and handle rewriting in hypergraphs.

The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.

In this paper, we prove that the category of rack crossed modules (with a fixed codomain) is finitely complete. other words, construct product, pullback and equalizer objects in racks. We therefore unify group-theoretical analogy completeness property sense functor $\mathbf{Conj \colon Grp \to Rack} $.