In this paper, we introduce two results. First we prove Lemma about the additivity and the multiplicativity. This Lemma states that for a unitary covariant channel Ψ and a channel M such that M(ρ0) is of rank one for some state ρ0 ∈ S(H) the additivity of the minimal output entropy of Ψ implies that of Ψ ◦ M , and the multiplicativity of the maximal output p-norm of Ψ, that of Ψ ◦M . Next we co...

In this paper, we study allocation problems and other related problems where a discrete estate should be divided among agents who have claims on it. We characterize the set of rules satisfying additivity on the estate along with additivity on the estate and the claims. These results complete the characterizations given by Bergantiños and Vidal-Puga (Mathematical Social Sciences) in the continuo...

We consider the problem of testing for additivity and joint effects in multivariate nonparametric regression when the data are modelled as observations of an unknown response function observed on a d-dimensional (d ≥ 2) lattice and contaminated with additive Gaussian noise. We propose tests for additivity and joint effects, appropriate for both homogeneous and inhomogeneous response functions, ...

Heterosis is the phenomenon whereby the progeny of particular inbred lines have enhanced agronomic performance relative to both parents. Although several hypotheses have been proposed to explain this fundamental biological phenomenon, the responsible molecular mechanisms have not been determined. The maize inbred lines B73 and Mo17 produce a heterotic F1 hybrid. Global patterns of gene expressi...

This study tested the hypothesis that endogenous glucocorticoids regulate a putative neurotransmitter function of corticotropin-releasing factor (CRF) in the locus coeruleus (LC). LC spontaneous discharge and activation by intracerebroventricularly administered CRF, hypotensive challenge, sciatic nerve stimulation, and carbachol were compared in adrenalectomized and sham-operated halothane-anes...

1. Human visual selectivity for direction of movement was determined using a subthreshold summation technique. 2. The threshold contrast for detecting a drifting sinusoidal grating was found to be independent of the contrast of an added subthreshold grating which moved in the opposite direction. 3. The detection threshold for a counterphase flickering grating is twice that for a moving grating,...

We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.

The nearest trapezoidal fuzzy number to a fuzzy number, with respect to a well-known metric and preserving the expected interval, was determined in recent articles. In the present paper the properties of additivity and continuity of the trapezoidal approximation operator are studied. Keywords— Additivity, Approximation, Continuity, Fuzzy number, Trapezoidal fuzzy number.