The new structure of K-recurrency naturally emerges from an invariance property of an old identity by Lovelock.doi:10.4064/cm122-1-7Mantica C. AMolinari L. GColloquium MathematicumMantica, C. A. and Molinari, A. G., A second-order identity for the Riemann tensor and applications, Coll....
A covariant second-order differential identity for the Riemann tensor is derived from the Bianchi identities, on a manifold with symmetric connection. MSC class: 53A45, 53B20. PACS numbers: 1 Given a symmetric connection Γc = Γc on a manifold, one has the notion of covariant ab ba...
, 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....
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...
www.nature.com/scientificreports OPEN Ab initio molecular dynamics of liquid water using embedded- fragment second-order many-body received: 30 March 2015 perturbation theory towards itsaccepted: 28August 2015 accurate property predictionPublished: 24 September 2015 Soohaeng Yoo Willow1,2,3, ...
For first-order equations, in [4] a rank-adaptive variant of the unconventional integrator [5] was proposed. However, the approach from [4] is not applicable to the projector-splitting integrator [19]. In [8], rank-adaptivity for tensor methods for high-dimensional PDEs was based on a ...
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...
{\prime} }\)have a tensor product structure. Separable states onABare defined as those that admit a decomposition as in equation (1). A positive trace-preserving operation\({{\varLambda }}:{{{\mathcal{T}}}({{{\mathcal{H}}}_{A}\otimes {{{\mathcal{H}}}_{B})\to {{{\mathca...
Sipe2 We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order optical conductivities, calculated from the...
Consider a second order hyperbolic equation in of the form (1.1) where is the time variable. In (1.1) , where is the metric tensor, is the vector potential. We assume that all coefficients in (1.1) belong to and that (1.2) Let be dual variables to . The strict hyperbolicity of ...