We examine gravitational wave memory in the case where sources and detector are in an expanding cosmology. For simplicity, we treat the case where the cosmology is de Sitter spacetime, and discuss the possibility of generalizing our results to the case of a more realistic cosmology. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime, but with the magnitude of the effect multiplied by a redshift factor.

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In this paper, we show that general homogeneous manifolds G/P satisfy Conjecture O of Galkin, Golyshev and Iritani which `underlies' Gamma conjectures I and II of them. Our main tools are the quantum Chevalley formula for G/P and a theory on nonnegative matrices including Perron-Frobenius theorem.

Let$M$be a ($n$−1)-dimensional manifold in$R$^{$n$}with non-vanishing Gaussian curvature. Using an estimate established in the early work of the author [4], we will improve the known result of Y. Domar on the weak spectral synthesis property by reducing the smoothness assumption upon the manifold$M$. Also as an application of the method, a uniqueness property for partial differential equations with constant coefficients will be proved, which for some specific cases recovers or improves Hörmander's general result.

In this paper, we describe all (2,3)-torus structures of a highly symmetric 39-cuspidal degree 12 curve. A direct computer-aided determination of these torus structures seems to be out of reach. We use various quotients by automorphisms to find torus structures. We use a height pairing argument to show that there are no further structures.