Milan Hladnik

Cyclic Haar graphs

For a given group Γ with a generating set A, a dipole with |A| parallel arcs (directed edges) labeled by elements of A gives rise to a voltage graph whose covering graph, denoted by H(Γ,A) is a bipartite, regular graph, called a bi-Cayley graph. In the case when Γ is abelian we refer to H(Γ,A) as the Haar graph of Γ with respect to the symbol A. In particular for Γ cyclic the above graph is referred to as a cyclic Haar graph. A basic theory of cyclic Haar graphs is presented.

Ab initio calculation of magnetic shielding with a finite perturbation method

Abstract Fluorine and proton magnetic shieldings of HF are calculated with the use of an ab initio finite perturbation molecular orbital theory with four different basis sets of gauge invariant atomic orbitals.

SCHUR NORMS OF BICIRCULANT MATRICES

Abstract A formula is given for computing Schur norm of a block-circulant matrix with circulant blocks together with some generalizations.

Susceptibility and magnetic shieldings of the BH molecule

Abstract Susceptibility and magnetic shieldings of both nuclei of BH are calculated by use of the finite perturbation method and gauge invariant gaussian basis sets. The results provide further evidence for the temperature independent paramagnetism of BH.

Compact Schur multipliers

Compact Schur multipliers on the algebra B(t) of all bounded linear operators on an infinite-dimensional separable complex Hilbert space 7will be identified as the elements of the Haagerup tensor product co 9h Co (the completion of co (&co in the Haagerup norm). Other ideals of Schur multipliers related to compact operators will also be characterized.

Ab initio calculation of magnetic shielding and susceptibility. Finite perturbation calculation of susceptibility with GIAO's

Abstract The magnetic susceptibility of hydrogen fluoride is calculated with four different basis sets of gauge invariant atomic orbitals (GIAOs). The Roothaan equations are solved for various values of the magnetic field strength and the susceptibility is deduced by a numerical differentiation of the energy.

Trace-preserving homomorphisms of semigroups

Abstract We consider those homomorphisms φ of semigroups of trace-class operators on a Hilbert space that preserve trace. If φ is a spatially induced isomorphism on a semigroup S , that is φ(S)T=TS for an invertible operator T and for all S in S , then φ clearly has this property. More generally, if T in the relation above is a densely defined, closed, injective operator with dense image, φ still preserves trace. We prove the converse of this statement under certain conditions. Using these results we prove simultaneous similarity theorems for semigroups of operators (on finite or infinite-dimensional spaces) whose members are individually similar to unitary or J-unitary operators.

Products of roots of the identity

It is proved that every invertible bounded linear operator on a complex infinite-dimensional Hilbert space is a product of five n-th roots of the identity for every n > 2. For invertible normal operators four factors suffice in general.

Finite Perturbation Studies of Magnetic Susceptibility and Shielding with GIAO

Abstract The magnetic susceptibility tensor and proton and fluorine magnetic shielding tensors are cal culated for F2 and (FHF)- using an ab initio finite perturbation method with gauge-invariant atomic orbitals (GIAO). The discussion of the basis set deficiency shows that the calculated values for the susceptibilities are reliable. Simple additivity (Pascal rule) for the susceptibility is con firmed.