In this representation (derived from the second moment tensor analysis
Bayesian Tensor Analysis
// IEEE International Joint Conference on Neural Networks (IJCNN).--2008.
Crack classification for three AE events were performed by AE parameters and by moment tensor analysis
. In Figure 10, crack classification by AE parameters, RA value and Average Frequency was performed by two sensors.
Vekua, The Basics of Tensor Analysis
and Theory of Covariants, Nauka, Moscow, Russia, 1978 (Russian).
For students of mechanics, mathematics, and physics, Fomenko and Muishchenko (both mechanics and mathematics, Moscow State U.) explain the basics of general topology, nonlinear coordinate systems, the theory of smooth manifolds, the theory of curves and surfaces, transformation groups, tensor analysis
and Riemannian geometry, the theory of integration and homologies, fundamental groups, and variational problems of Riemannian geometry.
Sokolnikoff, Tensor Analysis
Theory and Applications to Geometry and Mechanics of Continua, John Wiley & Sons, Inc., New York (1964).
PC Macsyma performs basic and matrix algebra and trigonometry, differential and integral calculus, and vector and tensor analysis
. Its symbolic functions allow calculation of differential and integral equations, Laplace and Fourier transforms, vector and tensor calculus, and finite difference equations.
He writes for graduate and senior undergraduate students and for scientists interested in quantitative seismology, and assumes knowledge of linear algebra, differential and integral calculus, vector calculus, tensor analysis
, and ordinary and partial differential equations.
It is for beginning graduate and advanced undergraduate students who have a background in elementary calculus and differential equations, linear algebra, complex analysis, and vector and tensor analysis
. He shies away from the coordinate system and components of vectors and tensors whenever possible, and uses the Einstein summation convention extensively.
Material is arranged in sections beginning with vector and tensor algebra, vector and tensor analysis
, and kinematics, and ending with large-deformation theory of isotropic plastic solids, and theory of single crystals undergoing small and large deformations.
AE source mechanisms in engineering materials can be kinematically identified by applying the moment tensor analysis
of AE signal-based methods (Grosse and Ohtsu, 2008).
Students should have completed a solid lower-division course in classical mechanics and have a good working knowledge of multivariable calculus, vector calculus, some linear algebra, some complex variable theory, elements of ordinary and partial differential equations, and introductory tensor analysis
. ([umlaut] Ringgold, Inc., Portland, OR)