Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Studying Coxiella burnetii Type IV Substrates in the Yeast Saccharomyces cerevisiae: Focus on Subcellular Localization and Protein Aggregation.

Coxiella burnetii is a Gram-negative obligate parasitic bacterium that causes the disease Q-fever in humans. To establish its intracellular niche, it utilizes the Icm/Dot type IVB secretion system (T4BSS) to inject protein effectors into the host cell cytoplasm. The host targets of most cognate and candidate T4BSS-translocated effectors remain obscure. We used the yeast Saccharomyces cerevisiae as a model to express and study six C. burnetii effectors, namely AnkA, AnkB, AnkF, CBU0077, CaeA and CaeB, in search for clues about their role in C. burnetii virulence. When ectopically expressed in HeLa cells, these effectors displayed distinct subcellular localizations. Accordingly, GFP fusions of these proteins produced in yeast also decorated distinct compartments, and most of them altered cell growth. CaeA was ubiquitinated both in yeast and mammalian cells and, in S. cerevisiae, accumulated at juxtanuclear quality-control compartments (JUNQs) and insoluble protein deposits (IPODs), characteristic of aggregative or misfolded proteins. AnkA, which was not ubiquitinated, accumulated exclusively at the IPOD. CaeA, but not AnkA or the other effectors, caused oxidative damage in yeast. We discuss that CaeA and AnkA behavior in yeast may rather reflect misfolding than recognition of conserved targets in the heterologous system. In contrast, CBU0077 accumulated at vacuolar membranes and abnormal ER extensions, suggesting that it interferes with vesicular traffic, whereas AnkB associated with the yeast nucleolus. Both effectors shared common localization features in HeLa and yeast cells. Our results support the idea that C. burnetii T4BSS effectors manipulate multiple host cell targets, which can be conserved in higher and lower eukaryotic cells. However, the behavior of CaeA and AnkA prompt us to conclude that heterologous protein aggregation and proteostatic stress can be a limitation to be considered when using the yeast model to assess the function of bacterial effectors.

Expansible Computable Aggregation Rules

The aggregation operator have been considered from a computable point of view. The important condition that the computation is friendly when portions of data are inserted o deleted to the list of values to aggregate is considered.

A continuous model for quasinilpotent operators.

A classical result due to Foias and Pearcy establishes a discrete model for every quasinilpotent operator acting on a separable, infinite-dimensional complex Hilbert space HH . More precisely, given a quasinilpotent operator T on HH , there exists a compact quasinilpotent operator K in HH such that T is similar to a part of K⊕K⊕⋯⊕K⊕⋯K⊕K⊕⋯⊕K⊕⋯ acting on the direct sum of countably many copies of HH . We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0C0 -semigroups of quasinilpotent operators.

The spectra of linear fractional composition operators on weighted Dirichlet spaces

We completely determine the spectra of composition operators induced by linear fractional self-maps of the unit disc acting on weighted Dirichlet spaces; extending earlier results by Higdon [8] and answering the open questions in this context.

Rota’s universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Strictly singular operators in pairs of L (p) space

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L (q) is found. There exists a strictly singular but not superstrictly singular operator on L (p) , provided that p not equal 2.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.