We analyze the state/trajectory tracking problem using Lyapunov control for finite-dimensional quantum systems when the target state is not a generic density operator and the Lyapunov function is therefore not a Morse function. For ideal systems general stability results are derived for stationary target states based on the linearization method. For the special class of pseudo-pure states a ful...

In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of RR into R (N) R can be extended to RR. Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is...

For each d, we construct CAT(0) cube complexes on which Cremona groups of rank d act by isometries. From these actions deduce new and old group-theoretical dynamical results about groups. In particular, study the behavior irreducible components exceptional loci. This leads to proofs regularization theorems, such as with property FW. We also find constraints degree growth for non-pseudo-regulari...

After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W ⊂ GL(V ) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural representations of W , through a ‘periodic’ family of representations of its braid group. We also prove that, when W is irreducible, then the squares of definin...

We present in this paper a covariant quantization of the “massive” vector field on de Sitter (dS) space based on analyticity in the complexified pseudo-Riemanian manifold. The correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time is essential in our approach. We introduce the Wightman-Gärding axiomatic for vector field on ...

Consider an ideal I ⊂ R = C[x 1 ,. .. , x n ] defining a complex affine variety X ⊂ C n. We describe the components associated to I by means of numerical primary decomposition (NPD). The method is based on the construction of deflation ideal I (d) that defines the deflated variety X (d) in a complex space of higher dimension. For every embedded component there exists d and an isolated component...

This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We st...

The irreducible representations of the double cover of SL(m) with infinitesmal character 1p having a maximal primitive ideal are determined. We investigate whether these representations are attached to a nilpotent orbit and use the orbit method to speculate their K types. We conclude with a character formula expressing the representations as a sum of simpler virtual representions. Thesis Superv...

Zadoff-Chu (ZC) sequences have been used as synchronization sequences in modern wireless communication systems, replacing the conventional pseudo-random noise (PN) sequences due to their perfect autocorrelation properties. We first study the ambiguity problem between a timing offset and a frequency offset when a ZC sequence is used as a synchronization signal. We show how a frequency offset can...