Quantum-mechanical calculation of the fourth-order tensor X(4)D (wa; w1, w1, w1, -w2) for a nonracemic solution of chiral molecules

1995 ◽  
Author(s):  
N. I. Konovalov ◽  
Tamara M. Il'inova ◽  
A. V. Karzanov ◽  
Nikolai I. Koroteev
Keyword(s):  
Fourth Order ◽  
Quantum Mechanical Calculation ◽  
Quantum Mechanical ◽  
Chiral Molecules ◽  
Order Tensor ◽  
Mechanical Calculation ◽  
Fourth Order Tensor

scholarly journals Integrity basis for a second-order and a fourth-order tensor

1982 ◽  
Vol 5 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Josef Betten
Keyword(s):  
Fourth Order ◽  
Second Order ◽  
Tensor Function ◽  
Order Tensor ◽  
Isotropic Tensor ◽  
Anisotropic Properties ◽  
Isotropic Tensor Function ◽  
Fourth Order Tensor

In this paper a scalar-valued isotropic tensor function is considered, the variables of which are constitutive tensors of orders two and four, for instance, characterizing the anisotropic properties of a material. Therefore, the system of irreducible invariants of a fourth-order tensor is constructed. Furthermore, the joint or simultaneous invariants of a second-order and a fourth-order tensor are found. In a similar way one can construct an integrity basis for a tensor of order greater than four, as shown in the paper, for instance, for a tensor of order six.

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