Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

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Low-Rank Tensor Methods for High-Dimensional Problems

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In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

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The high-efficiency silicon heterojunction (SHJ) technology is now perceived mature enough to enter the Giga-Watt manufacturing scale with several players around the globe. The growth of the SHJ technology requires confidence from manufacturers, investors, ...

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Rank-Adaptive Time Integration Of Tree Tensor Networks

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A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves connection tenso ...

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The multivariate Serre conjecture ring

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It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

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Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

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The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

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Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

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Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups

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Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...

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Multiplicity-free representations of algebraic groups II

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The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

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Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Alfio Quarteroni, Francesco Regazzoni

Elsevier Science Sa2023