Effective rationality of second-order symmetric tensor spaces

Author(s):  
M. Olive ◽  
R. Desmorat
2006 ◽  
Vol 83 (2) ◽  
pp. 191-204 ◽  
Author(s):  
Claude Vallée ◽  
Qi-Chang He ◽  
Camelia Lerintiu

Author(s):  
Sombuddha Bhattacharyya ◽  
Tuhin Ghosh

AbstractThis article offers a study of the Calderón type inverse problem of determining up to second order coefficients of higher order elliptic operators. Here we show that it is possible to determine an anisotropic second order perturbation given by a symmetric matrix, along with a first order perturbation given by a vector field and a zero-th order potential function inside a bounded domain, by measuring the Dirichlet to Neumann map of the perturbed biharmonic operator on the boundary of that domain.


2018 ◽  
Vol 27 (07) ◽  
pp. 1841003 ◽  
Author(s):  
Jerzy Kocik

An alternative framework underlying connection between tensor [Formula: see text]-calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for the diagrammatic recoupling methods. Yet, it preserves the standard chromatic graph evaluations. In contrast with the standard formulation, the background space is that of symmetric tensor spaces, which seems to be in accordance with the representation theory of [Formula: see text]. An example of Apollonian disk packing is shown to be a source of spin networks. The graph labeling is extended to non-integer values, resulting in the complex values of chromatic evaluations.


2010 ◽  
Vol 15 (4) ◽  
pp. 533-545
Author(s):  
Nikolay Vabishchevich ◽  
Petr Vabishchevich

Mathematical physics problems are often formulated using differential operators of vector analysis, i.e. invariant operators of first order, namely, divergence, gradient and rotor (curl) operators. In approximation of such problems it is natural to employ similar operator formulations for grid problems. The VAGO (Vector Analysis Grid Operators) method is based on such a methodology. In this paper the vector analysis difference operators are constructed using the Delaunay triangulation and the Voronoi diagrams. Further the VAGO method is used to solve approximately boundary value problems for the general elliptic equation of second order. In the convection‐diffusion‐reaction equation the diffusion coefficient is a symmetric tensor of second order.


Author(s):  
W. L. Bell

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.


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