Search results for "Tensor"
showing 10 items of 550 documents
Orbital Decomposition of the Carbon Chemical Shielding Tensor in Gold(I) N-Heterocyclic Carbene Complexes.
2020
The good performance of N‐heterocyclic carbenes (NHCs), in terms of versatility and selectivity, has called the attention of experimentalists and theoreticians attempting to understand their electronic properties. Analyses of the Au(I)–C bond in [(NHC)AuL]+/0 (L stands for a neutral or negatively charged ligand), through the Dewar–Chatt–Duncanson model and the charge displacement function, have revealed that NHC is not purely a σ‐donor but may have a significant π‐acceptor character. It turns out, however, that only the σ‐donation bonding component strongly correlates with one specific component of the chemical shielding tensor. Here, in extension to earlier works, a current density analysi…
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions
2010
Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.
A note on the higher order strain and stress tensors within deformation gradient elasticity theories: Physical interpretations and comparisons
2016
Abstract Higher order strain and stress tensors encompassed within gradient elasticity theories are discussed with a particular concern to the physical meaning of double and triple stresses. A single rule is shown to hold for the physical interpretation of the indices of a higher order stress tensor both within distortion gradient and strain gradient theories, whereas the analogous Mindlin’s rule holds only within distortion gradient theories. Double and triple stresses are discussed separately with the aid of simple illustrative examples. A corrigendum to a previous paper by the author (IJSS 50 (2013) 3749–3765) is also presented.
A shallow water model with eddy viscosity for basins with varying bottom topography
2001
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.
A nonhomogeneous nonlocal elasticity model
2006
Nonlocal elasticity with nonhomogeneous elastic moduli and internal length is addressed within a thermodynamic framework suitable to cope with continuum nonlocality. The Clausius–Duhem inequality, enriched by the energy residual, is used to derive the state equations and all other thermodynamic restrictions upon the constitutive equations. A phenomenological nonhomogeneous nonlocal (strain difference-dependent) elasticity model is proposed, in which the stress is the sum of two contributions, local and nonlocal, respectively governed by the standard elastic moduli tensor and the (symmetric positive-definite) nonlocal stiffness tensor. The inhomogeneities of the elastic moduli and of the int…
Comparison of electron diffraction data from non-linear optically active organic DMABC crystals obtained at 100 and 300 kV
2000
During the recent past, we have synthesized a new class of molecules with intramolecular two-dimensional charge transfer upon excitation. The present report presents such a molecule, 2,6-bis(4-dimethylamino-benzylidene)-cyclohexanone (DMABC), with an unusually high value of the second-order non-linear optical (NLO) coefficients. In order to optimize the macroscopic NLO properties of the compounds, it is necessary to relate their first hyperpolarizability tensors at a molecular level to those at a crystal bulk level. This requires a complete structure determination and refinement. However, the growth of sufficiently large single crystals, which are needed for structural analysis and refineme…
Association between cingulum bundle structure and cognitive performance: an observational study in major depression.
2009
AbstractBackgroundMajor depression can be regarded as a systemic neurobehavioral disorder resulting from dysfunction of the limbic-cortical networks. The cingulum bundle represents a major association fiber tract of those networks. The aim of our study was to determine the association of brain structural tissue markers of the cingulum bundle and cognitive function in patients with major depression.MethodsRegion-of-interest-based analyses of the middle-anterior and middle-posterior cingulum bundle fractional anisotropy (FA) and mean diffusivity (MD) using color-coded diffusion-tensor imaging and neuropsychological assessment in 14 patients with major depression.ResultsFA of the middle-anteri…
Fast Matrix Multiplication
2015
Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time O(n2.3755). Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le~Gall has led to an improved algorithm running in time O(n2.3729). These algorithms are obtained by analyzing higher and higher tensor powers of a certain identity of Coppersmith and Winograd. We show that this exact approach cannot result in an algorithm with running time O(n2.3725), and identify a wide class of variants of this approach which cannot result in an algorithm with running time $O(n^{2.3078}); in particular, this approach cannot prove the conjecture that for every e > 0, …
Multicenter stability of diffusion tensor imaging measures: a European clinical and physical phantom study.
2011
Diffusion tensor imaging (DTI) detects white matter damage in neuro-psychiatric disorders, but data on reliability of DTI measures across more than two scanners are still missing. In this study we assessed multicenter reproducibility of DTI acquisitions based on a physical phantom as well as brain scans across 16 scanners. In addition, we performed DTI scans in a group of 26 patients with clinically probable Alzheimer's disease (AD) and 12 healthy elderly controls at one single center. We determined the variability of fractional anisotropy (FA) measures using manually placed regions of interest as well as automated tract based spatial statistics and deformation based analysis. The coefficie…
Central polynomials and matrix invariants
1996
LetK be a field, charK=0 andM n (K) the algebra ofn×n matrices overK. If λ=(λ1,…,λ m ) andμ=(μ 1,…,μ m ) are partitions ofn 2 let $$\begin{gathered} F^{\lambda ,\mu } = \sum\limits_{\sigma ,\tau \in S_n 2} {\left( {\operatorname{sgn} \sigma \tau } \right)x_\sigma (1) \cdot \cdot \cdot x_\sigma (\lambda _1 )^{y_\tau } (1)^{ \cdot \cdot \cdot } y_\tau (\mu _1 )^{x\sigma } (\lambda _1 + 1)} \hfill \\ \cdot \cdot \cdot x_\sigma (\lambda _1 + \lambda _2 )^{y_\tau } (\mu _1 ^{ + 1} )^{ \cdot \cdot \cdot y_\tau } (\mu _1 + \mu _2 ) \hfill \\ \cdot \cdot \cdot x_\sigma (\lambda _1 + \cdot \cdot \cdot + \lambda _{\mu - 1} ^{ + 1} ) \hfill \\ \cdot \cdot \cdot x_\sigma (n^2 )^{y_\tau } (\mu _1 ^{ + \…