Schur finiteness and nilpotency

Let A be a Q-linear pseudo-abelian rigid tensor category. A notion of finiteness due to Kimura and (independently) O'Sullivan guarantees that the ideal of numerically trivial endomorphism of an object is nilpotent. We generalize this result to special Schur-finite objects. In particular, in the category of Chow motives, if X is a smooth projective variety which satisfies the homological sign conjecture, then Kimura-finiteness, a special Schur-finiteness, and the nilpotency of CH^{ni}(X^i\times X^i)_{num} for all i (where n=dim X) are all equivalent

Spectral behavior of preconditioned non-Hermitian multilevel block Toeplitz matrices with matrix-valued symbol

This note is devoted to preconditioning strategies for non-Hermitian multilevel block Toeplitz linear systems associated with a multivariate Lebesgue integrable matrix-valued symbol. In particular, we consider special preconditioned matrices, where the preconditioner has a band multilevel block Toeplitz structure, and we complement known results on the localization of the spectrum with global distribution results for the eigenvalues of the preconditioned matrices. In this respect, our main result is as follows. Let $I_k:=(-\pi,\pi)^k$, let $\mathcal M_s$ be the linear space of complex $s\times s$ matrices, and let $f,g:I_k\to\mathcal M_s$ be functions whose components $f_{ij},\,g_{ij}:I_k\to\mathbb C,\ i,j=1,\ldots,s,$ belong to $L^\infty$. Consider the matrices $T_n^{-1}(g)T_n(f)$, where $n:=(n_1,\ldots,n_k)$ varies in $\mathbb N^k$ and $T_n(f),T_n(g)$ are the multilevel block Toeplitz matrices of size $n_1\cdots n_ks$ generated by $f,g$. Then $\{T_n^{-1}(g)T_n(f)\}_{n\in\mathbb N^k}\sim_\lambda g^{-1}f$, i.e. the family of matrices $\{T_n^{-1}(g)T_n(f)\}_{n\in\mathbb N^k}$ has a global (asymptotic) spectral distribution described by the function $g^{-1}f$, provided $g$ possesses certain properties (which ensure in particular the invertibility of $T_n^{-1}(g)$ for all $n$) and the following topological conditions are met: the essential range of $g^{-1}f$, defined as the union of the essential ranges of the eigenvalue functions $\lambda_j(g^{-1}f),\ j=1,\ldots,s$, does not disconnect the complex plane and has empty interior. This result generalizes the one obtained by Donatelli, Neytcheva, Serra-Capizzano in a previous work, concerning the non-preconditioned case $g=1$. The last part of this note is devoted to numerical experiments, which confirm the theoretical analysis and suggest the choice of optimal GMRES preconditioning techniques to be used for the considered linear systems.Comment: 18 pages, 26 figure

Development of a multifunctional panel for aerospace use through SLM additive manufacturing

Lattice materials can overcome the need of light and stiff structures in the aerospace industry. The wing leading edge is one of the most critical parts for both on-board subsystem and structure features: it must withstand to the aerodynamic loads and bird-strike, integrating also the anti-ice system functions. Nowadays, this part is made by different components bonded together such as external skin, internal passageways, and feeding tubes. In the present work, a single-piece multifunctional panel made by additive manufacturing will be developed. Optimal design and manufacturing are discussed according to technological constraints, aeronautical performances and sustainability

a comparison between 3d printing and milling process for a spar cap fitting wing fuselage of uav aircraft

Abstract Topology optimization is playing an important role in the aircraft design. The demand of lower fuel consumption reflects on the optimization of the airframe of flying vehicles to reduce the structure weight, therefore improving the fraction of the payload. This work focuses on the replacement of an existing part (spar cap fitting) with the new topologically optimized part to be manufactured with 3D printing (Selective Laser Sintering -SLS). The manufacturing constraints (minimum dimension, growth orientation) influence on the optimal results is evaluated to compare traditional milling process' performance with the new SLS technique

A Conceptual Framework for Comparing Alternative Commodities in the Energy Transition

The global emissions increase requires the adoption of proper countermeasures, aimed at tackling climate change. On the one hand, the transition towards a renewable-based energy sector is an undeferrable need, because of its important impact on the overall emissions balance. On the other hand, a single final use can be fed by more than one commodity, and their coexistence/competition paves the way to the development of a multi-commodity energy system, enabling the implementation of the so-called ”cross-sector integration”. In this paper, we propose a conceptual framework for the comparative assessment of the various energy commodity chains, aimed at defining the preferrable ones for residential and transport uses. The evaluation of their overall performance is carried out determining the quantity and the quality of the involved commodities, by adopting energy and exergy efficiency along the entire chain, provided that one unit of primary energy can supply one chain only. This straightforward assessment method is not constrained by any generation capacity and/or emission related targets and introduces a commodity-based evaluation framework, that differs from the already existing ones that adopt a technology-oriented approach

Crossmodal object-based attention: auditory objects affect visual processing

Abstract According to the object-based view, visual attention can be deployed to "objects" or perceptual units, regardless of spatial locations. Recently, however, the notion of object has also been extended to the auditory domain, with some authors suggesting possible interactions between visual and auditory objects. Here we show that task-irrelevant auditory objects may affect the deployment of visual attention, providing evidence that crossmodal links can also occur at an object-based level. Hence, in addition to the well documented control of visual objects over what we hear, our findings demonstrate that, in some cases, auditory objects can affect visual processing. q 2005 Elsevier B.V. All rights reserved. Keywords: Crossmodal attention; Object-based attention; Auditory objects; Sensory modalities Attention is an important cognitive function by means of which the human cognitive system is able to select the information relevant for the current behaviour. According to the "space-based" vie