Abstract. The first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right halfplane mapping or a normalized vertical strip mapping is convex in the direction of the real axis. provided that it is locally univalent. In this paper, we prove that in general the assumption of local univalency cannot be omitted. However, we are able to show that in some cases these harmonic convolutions are locally univalent. Using this we obtain interesting examples of univalent harmonic maps one of which is a map onto the plane with two parallel slits.

The neutrinoless double beta decay (0νββ-decay) transition to the first excited 0 + collective final state is examined for A=76, 82, 100 and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized Quasiparticle Random Phase Approximation. Transitions to the first excited twoquadrupole phonon 0 + state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the 0νββ-decay experiments. The half-life of 0νββ-decay to the first excited state 0 + 1 is by a factor of 10 to 100 larger than that of the transition to the ground state, 0 + g.s. .

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Heme oxygenase is a biological factor that might explain the relationship between inflammation, oxidative stress, and the biological and functional changes in brain activity in depression. HO-1 is a candidate depression biomarker and provides an avenue for novel preventative and diagnostic strategies against this disease.

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