(ii) Use of multiplier blocks can drastically change the complexity relations between different structures. Despite using almost twice the wordlength, and many more coefficients (corresponding to having almost 2.5 times the complexity using the C, measure), the direct forms require similar numbers of adders to the waveform. Similarly, but less dramatically, the cascade and parallel forms are si...

Let G be a complex symplectic group. We construct a certain Gvariety N, which shares many nice properties with the nilpotent cone of G. For example, it is normal, has finitely many G-orbits, and admits a G-equivariant resolution of singularity in a similar way to the Springer resolution. Our new G-variety admits an action of G× C × C instead of the G×C-action on the nilpotent cone. This enables...

It is shown that the Jacobian Conjecture holds for all polynomial maps F : k → k of the form F = x + H , such that JH is nilpotent and symmetric, when n ≤ 4. If H is also homogeneous a similar result is proved for all n ≤ 5. Introduction Let F := (F1, . . . , Fn) : C → C be a polynomial map i.e. each Fi is a polynomial in n variables over C. Denote by JF := (i ∂xj )1≤i,j≤n, the Jacobian matrix ...

τ(w)(x) = 〈x(w), w〉, w ∈ W, x ∈ g ⊆ End(W ), and similarly for τ ′. Our main theorem describes the behaviour of closures of nilpotent orbits under the action of moment maps. It is easy to see that for a nilpotent coadjoint orbit O ⊆ g∗ the set τ ′(τ−1(O)) is the union of nilpotent coadjoint orbits in g′. It turns out that it is a closure of a single orbit: Theorem 1.1 Let O ⊆ g∗ be a nilpotent ...

It is well known that the multiplier ideal J (r · a) of an ideal a determines in a straightforward way the multiplier ideal J (r ·f) of a sufficiently general element f of a. We give an explicit condition on a polynomial f ∈ C[x1, . . . , xn] which guarantees that it is a sufficiently general element of the most natural associated monomial ideal, the ideal generated by its terms. This allows us...

We show that every finitely generated nilpotent group of class 2 occurs as the quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup.