On Minimizing ||S−(AX−XB)||Pp

In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class

Spectral properties of (m;n)-isosymmetric multivariable operators

Inspired by recent works on $m$-isometric and $n$-symmetric multivariables operators on Hilbert spaces, in this paper we introduce the class of $(m, n)$-isosymmetric multivariables operators. This new class of operators emerges as a generalization of the $m$-isometric and $n$-isosymmetric multioperators. We study this class of operators and give some of their basic properties. In particular, we show that if ${\bf \large R} \in {\mathcal B}^{(d)}({\mathcal H})$ is an $(m,n )$-isosymmetric multioperators and ${\bf \large Q}\in {\mathcal B}^{(d)}({\mathcal H})$ is an $q$-nilpotent multioperators, then ${\bf\large R} +{\bf\large Q}$ is an $(m + 2q - 2,n+2q-1)$-isosymmetric multioperators under suitable conditions. Moreover, we give some results about the joint approximate spectrum of an $(m,n)$-isosymmetric multioperators

Impact of mosquito bites on asexual parasite density and gametocyte prevalence in asymptomatic chronic Plasmodium falciparum infections and correlation with IgE and IgG titers.

International audienceAn immunomodulatory role of arthropod saliva has been well documented, but evidence for an effect on Plasmodium sp. infectiousness remains controversial. Mosquito saliva may orient the immune response toward a Th2 profile, thereby priming a Th2 response against subsequent antigens, including Plasmodium. Orientation toward a Th1 versus a Th2 profile promotes IgG and IgE proliferation, respectively, where the former is crucial for the development of an efficient antiparasite immune response. Here we assessed the direct effect of mosquito bites on the density of Plasmodium falciparum asexual parasites and the prevalence of gametocytes in chronic, asymptomatic infections in a longitudinal cohort study of seasonal transmission. We additionally correlated these parasitological measures with IgE and IgG antiparasite and anti-salivary gland extract titers. The mosquito biting density was positively correlated with the asexual parasite density but not asexual parasite prevalence and was negatively correlated with gametocyte prevalence. Individual anti-salivary gland IgE titers were also negatively correlated with gametocyte carriage and were strongly positively correlated with antiparasite IgE titers, consistent with the hypothesis that mosquito bites predispose individuals to develop an IgE antiparasite response. We provide evidence that mosquito bites have an impact on asymptomatic infections and differentially so for the production of asexual and sexual parasites. An increased research focus on the immunological impact of mosquito bites during asymptomatic infections is warranted, to establish whether strategies targeting the immune response to saliva can reduce the duration of infection and the onward transmission of the parasite

Some versions of Anderson's and Maher's inequalities II

We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel

Filomat 22:2 (2008), 1–8 THE NUMERICAL RANGE OF LINEAR OPERATORS

We offer a simple proof that convexoid operators on Hilbert space are normaloid, and given an example to show that the converse fails.