We prove a sharp bilinear estimate for the one dimensional Klein– Gordon equation. The proof involves an unlikely combination of five trigonometric identities. We also prove new estimates for the restriction of the Fourier transform to the hyperbola, where the pullback measure is not assumed to be compactly supported.

We determine the Chow rings of the complex algebraic groups E6 and E7, giving the explicit generators represented by the pullback images of Schubert varieties of the corresponding flag varieties. This is a continuation of the work of R. Marlin on the computation of the Chow rings of SOn(C), Spinn(C), G2, and F4.

The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square–integral of the wind forcing and the β parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical ...

We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in the C(ℵ)-fibration property. We give and prove the relationship between the C(ℵ)-fibration property and an approximate fibration property. Furthermore, we study the pullback maps for C(ℵ)-fibrations.

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.