4,899 research outputs found
Intersection products for tensor triangular Chow groups
We show that under favorable circumstances, one can construct an intersection
product on the Chow groups of a tensor triangulated category (as
defined by Balmer) which generalizes the usual intersection product on a
non-singular algebraic variety. Our construction depends on the choice of an
algebraic model for (a tensor Frobenius pair), which has to
satisfy a -theoretic regularity condition analogous to the Gersten
conjecture from algebraic geometry. In this situation, we are able to prove an
analogue of the Bloch formula and use it to define an intersection product
similar to a construction by Grayson. We then recover the usual intersection
product on a non-singular algebraic variety assuming a -theoretic
compatibility condition.Comment: 34 page
Totally geodesic submanifolds of the complex and the quaternionic 2-Grassmannians
In this article, I classify the totally geodesic submanifolds in the complex
2-Grassmannians and in the quaternionic 2-Grassmannians. It turns out that for
both of these spaces, the earlier classification of maximal totally geodesic
submanifolds in Riemannian symmetric spaces of rank 2, published by Chen and
Nagano (B.-Y. Chen, T. Nagano, "Totally geodesic submanifolds of symmetric
spaces, II", Duke Math. J. 45 (1978), 405--425) is incomplete.
For example, G_2(H^n) with n >= 7 contains totally geodesic submanifolds
isometric to a HP^2, its metric scaled such that the minimal sectional
curvature is 1/5; they are maximal in G_2(H^7). Also G_2(C^n) with n >= 6
contains totally geodesic submanifolds which are isometric to a CP^2 contained
in the HP^2 mentioned above; they are maximal in G_2(C^6). Neither submanifolds
are mentioned in the cited paper by Chen and Nagano
Minimal Radiative Neutrino Masses
We conduct a systematic search for neutrino mass models which only
radiatively produce the dimension-5 Weinberg operator. We thereby do not allow
for additional symmetries beyond the Standard Model gauge symmetry and we
restrict ourselves to minimal models. We also include stable fractionally
charged and coloured particles in our search. Additionally, we proof that there
is a unique model with three new fermionic representations where no new scalars
are required to generate neutrino masses at loop level. This model further has
a potential dark matter candidate and introduces a general mechanism for
loop-suppression of the neutrino mass via a fermionic ladderComment: final version as published in JHE
On the Funk transform on compact symmetric spaces
We prove that a function on an irreducible compact symmetric space M, which
is not a sphere, is determined by its integrals over the shortest closed
geodesics in M. We also prove a support theorem for the Funk transform on rank
one symmetric spaces which are not spheres.Comment: 8 page
Balanced data assimilation for highly-oscillatory mechanical systems
Data assimilation algorithms are used to estimate the states of a dynamical
system using partial and noisy observations. The ensemble Kalman filter has
become a popular data assimilation scheme due to its simplicity and robustness
for a wide range of application areas. Nevertheless, the ensemble Kalman filter
also has limitations due to its inherent Gaussian and linearity assumptions.
These limitations can manifest themselves in dynamically inconsistent state
estimates. We investigate this issue in this paper for highly oscillatory
Hamiltonian systems with a dynamical behavior which satisfies certain balance
relations. We first demonstrate that the standard ensemble Kalman filter can
lead to estimates which do not satisfy those balance relations, ultimately
leading to filter divergence. We also propose two remedies for this phenomenon
in terms of blended time-stepping schemes and ensemble-based penalty methods.
The effect of these modifications to the standard ensemble Kalman filter are
discussed and demonstrated numerically for two model scenarios. First, we
consider balanced motion for highly oscillatory Hamiltonian systems and,
second, we investigate thermally embedded highly oscillatory Hamiltonian
systems. The first scenario is relevant for applications from meteorology while
the second scenario is relevant for applications of data assimilation to
molecular dynamics
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