Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r -fold forms. The hyperbolizations depend on 2 r 1 arbitrary timelike vectors. The importance of the so-called "superenergy" tensors, which provide the ...
If one puts 2n pairs of symmetric points on the unit sphere of ℓ2n, where the points are chosen independently and are distributed uniformly on that sphere, and then takes the symmetric convex hull of the union of these points with the unit vector basis, one obtains a unit ball for a ...
I attempted to split a tensor of shape BxCxHxW into H tensors of shape BxCxW, performed DWT1DForward on each of them separately, and then concatenated the results. Unfortunately, I found that this approach is much slower than performing DWT2DForward, as demonstrated by the following code: ...
Some new explicit examples of nonhomogeneous irreducible Riemannian manifolds are given which are semi-symmetric and in a special case also curvature homogeneous. In particular, one obtains an infinite dimensional family of locally nonisometric complete metrics on 3 with the same curvature tensor as th...
deftorch_pad_reflect(image:torch.Tensor,paddings:Sequence[int])->torch.Tensor:paddings=np.array(paddings,dtype=int)assertnp.all(np.array(image.shape[-2:])>1),"Image shape should be more than 1 pixel"assertnp.all(paddings>=0),"Negative paddings not supported"whilenp.any(paddings):image_li...
Counting the degrees of freedom within the original higher dimensional metric, the reduction of a spin-2 bulk field results in three distinct classes of towers of KK modes: symmetric tensor, vector fields and scalar fields. The KK zero-mode fields are massless, while the excitation states ...
\end{aligned}$$ assume to have a sequence of symmetric functions \(h^n_\phi \in h^{2+2\epsilon }({\mathbb {s}}^2 \times {\mathbb {s}}^2)\) , \(n \in {\mathbb {n}}\) that approximates \(h_\phi \) in the following sense: $$\begin{aligned} \lim _{n \rightarrow...
Projectively flat surfaces, null parallel distributions, and conformally symmetric manifolds We determine the local structure of all pseudo-Riemannian manifolds of dimensions greater than 3 whose Weyl conformal tensor is parallel and has rank 1 whe... D Andrzej,R Witold - 《東北數學雜誌. second ser...
Based on lectures at the University of Illinois at Urbana-Champaign, Mackay and Tyson treat the conformal dimension, which measures the extent to which dimensions of a metric space can be reduced by quasi-symmetric deformations. Their survey covers definitions, classes of mappings between metric ...
a manifestly symmetric matrix. This is just one example, but I have found it to be true of all the anomalous di- mension matrices calculated to date. It is true not only for the anomalous dimension matrices of the virtual matrix elements, but also those for energy flow observables, ...