A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds with Recurrent or Symmetric structures are discussed. The new...
A second-order identity for the Riemann tensor Carlo Alberto Mantica and Luca Guido Molinari1 1 Dipartimento di Fisica, Universit` degli Studi di Milano, a and INFN, sezione di Milano, Via Celoria 16, I-20133 Milano, Italy arXiv:0802.0650v1 [math.DG] 5 Feb 2008 Abstract A ...
, fourth order tensor Nonlinear eigenvalue problem (looks like the KKT condtions): H(X)X = XΛ X ∗ X = I 19/32 Cryo-electron microscopy reconstruction Find 3D structure given samples of 2D images. Thanks: Amit Singer min R i N i =1 R i c ij − R j c ji 2 2 , s.t....
iωt Tr[α(0)]Tr[α (t) ] , −∞ (4) ∫IRanamisoan (ω) ∝ 2ω 15 kBT ∞ dt e−iωt Tr[β(0) ⋅ β (t) ] , −∞ (5) where α is the polarizability tensor of the unit cell and β = α − Tr[α]I/3 with I being the identity tensor....
The method of homogeneous deformation was combined with first-principles total-energy calculations to provide a general method for determining second- and third-order elastic constants for single crystals of arbitrary symmetry. Lagrangian strain tensors characterized by a single strain parameter are applied...
Both the projector-splitting integrator and the unconventional robust integrator have been successfully adapted to first-order tensor differential equations, cf. [6, 20, 21] and references therein. We are confident that the strategy for the adaptive algorithm for matrix differential equations also works...
We first derive five new Kubo formulae that express second-order transport coefficients in terms of three-point correlators of the stress tensor. We then apply these Kubo formulae to a large class of non-conformal holographic fluids at infinite coupling. We find strong evidence that the Haack鈥...
symmetric part of the Ricci tensor enters in L. [In the second order, purely metric, form (where Γ a µν is the Christoffel symbol) the 2D L is a total divergence – the Euler density, but that is not our point here.] In, and only in, 2D, our L is manifestly Weyl invari...
However, a second-order attention weighting would require parametrization by a tensor of degree three (3), which would take the parameter count of the model to O (m3), as both the input and the context vectors are of dimension m. For token representations of even modest size, this would ...
The matrix T can be diagonalized to obtain the three eigenvalues, αi (i = 1, 2, 3), of this tensor. The asphericity (δ) [28–31] has been used to characterize protein shapes, and is computed as 13 12 23 13 (1 ...