LetM be a tensor category with coefficients in a fieldK of characteristic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that the tensor product ⊗ of M is bilinear. Then symmetric and exterior powers of an object M ∈ M make sense, by using appropriate projectors relative to the action of the symmetric groups on tensor powers of M . One may therefore introduce the zeta fu...

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of th...

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence guarantees are established for third order tensors of rank k in d dimensions, wh...

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

consider the following consistent sylvester tensor equation[mathscr{x}times_1 a +mathscr{x}times_2 b+mathscr{x}times_3 c=mathscr{d},]where the matrices $a,b, c$ and the tensor $mathscr{d}$ are given and $mathscr{x}$ is the unknown tensor. the current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and ...

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between lowrank CP decomposition through gradient ascent (a variant of the tensor power method), and hard thresholding of the residual. We prove convergence to the globally optimal solution under natural incoh...

In this paper, we explore a novel observational signature of gravitational corrections during slow-roll inflation. We study the coupling of the inflaton field to highercurvature tensors in models with a minimal breaking of conformal symmetry. In that case, the most general correction to the tensor two-point function is captured by a coupling to the square of the Weyl tensor. We show that these ...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

Scalar spectra which exhibit a sharp drop in power at length scales corresponding to the Hubble radius today are known to lead to a better fit of the observed Cosmic Microwave Background (CMB) anisotropies, when compared to the conventional, featureless, power law spectrum. Recently, we have shown that scalar spectra with lower power on large scales naturally occur in punctuated inflation, i.e....