Let A be a symmetric k-algebra over a perfect field k. Külshammer defined for any integer n a mapping ζn on the degree 0 Hochschild cohomology and a mapping κn on the degree 0 Hochschild homology of A as adjoint mappings of the respective p-power mappings with respect to the symmetrizing bilinear form. In an earlier paper it is shown that ζn is invariant under derived equivalences. In the prese...

Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator [14]. For bilinear quantum control problems, no general results are available to fully determine when this mapping is singular or not. In this paper we give sufficient conditions, in terms of elements of the evolution semigroup, for a traje...

Recent GPU advances have popularized pixel-shader based techniques for per-pixel displacement mapping. An important step in the process is to compute intersection of ray with a bilinear patch approximating the displacement map. Accurate ray-patch intersection can significantly enhance the quality of rendered images. However, the increase in quality comes at a significant computation cost result...

We give a simple and efficient construction of a verifiable random function (VRF) on groups equipped with a bilinear mapping. Our construction is direct; it bypasses an expensive Goldreich-Levin transformation from a unique signature to a VRF in contrast to prior works of Micali-Rabin-Vadhan [MRV99] and Lysyanskaya [Lys02]. Our proofs of security are based on a decisional bilinear Diffie-Hellma...

In this paper we establish mapping properties of bilinear Coifman-Meyer multipliers acting on the product spaces H1(Rn)×bmo(Rn) and Lp(Rn)×bmo(Rn), with 1<p<∞. As application these results, obtain some related Kato-Ponce-type inequalities involving endpoint space bmo(Rn), also study pointwise a function in bmo(Rn) functions H1(Rn), h1(Rn) Lp(Rn),

We learn a mapping that negates adjectives by predicting an adjective’s antonym in an arbitrary word embedding model. We show that both linear models and neural networks improve on this task when they have access to a vector representing the semantic domain of the input word, e.g. a centroid of temperature words when predicting the antonym of ‘cold’. We introduce a continuous class-conditional ...

We consider a linear Schrödinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric eld (the control). We prove the exact controllability of this system, in any positive time, locally around the ground state. Similar results were proved for particular models [14, 15, 17], in non optimal spaces, in long time and the proof relied on the Nash-...

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bilinear and commutative mapping on the solution space, is studied. This family of PDE’s contains the Cauchy–Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebrai...

We decompose a matrix Y into a sum of rank one bilinear forms in a stepwise manner, by considering Y as a mapping from the finite dimensional space l r to the space l p . We provide transition formulas, and represent them in a duality diagram, thus generalizing the well known duality diagram in the french school of data analysis. As an application, we introduce a family of Euclidean multidimens...