Q |f − fQ|dx < ∞, (1) where |Q| is the n-dimensional Lebesgue measure of Q, fQ = |Q|−1 ∫ Q fdx, and the supremum is taken over all closed cubes Q ⊂ D with sides parallel to the coordinate axes. Let D and D′ be subdomains of Rm and Rn, m, n ≥ 1, respectively. We say that a map F : D → D′ is measurable if F−1(E) is measurable for each measurable subset E of D′. We say that a measurable map F : D ...

The present study investigates the time course and pattern of movement representation recovery in the motor cortex during the recovery after a peripheral paralysis. To this end a transitory flaccid paralysis of the vibrissae muscle was induced in adult rats that underwent two unilateral injections of 8 U of botulinum toxin (BTX) into a vibrissal pad, at a duration of 12 days from one another. T...

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since no...

For an (m+1)-dimensional space-time (X, g), define a mapped null hypersurface to be a smooth map ν : N → X (that is not necessarily an immersion) such that there exists a smooth field of null lines along ν that are both tangent and g-orthogonal to ν. We study relations between mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle ST M of an immersed spacelike hypersurf...

the blow-up of |KC +D| along the image of C (which we will also denote by C). In contrast, the Serre correspondence is a morphism only when d ≤ 2, as it is undefined at points of C (and certain secant varieties) for larger values of d. The structure of the Serre correspondence for large d (particularly d > 2g − 2, in which case it is dominant) is, however, well understood now, due largely to re...