Search results for "Isotropic quadratic form"
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Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form
1968
Abstract : A method is presented for the calculation of lower bounds to eigenvalues of operators that arise from variational problems for one quadratic form relative to a positive definite quadratic form. Eigenvalue problems of this kind occur, for example, in the theory of buckling of continuous linear elastic systems. The technique used is a modification of one introduced earlier, (1) sections II and IVB, for the determination of lower bounds to eigenvalues of semi-bounded self-adjoint operators. Other methods for the latter problem can be carried over without essential changes. The particular difficulty in the case we consider is that some operators which enter the calculation for the lo…
Quadratic rational solvable groups
2012
Abstract A finite group G is quadratic rational if all its irreducible characters are either rational or quadratic. If G is a quadratic rational solvable group, we show that the prime divisors of | G | lie in { 2 , 3 , 5 , 7 , 13 } , and no prime can be removed from this list. More generally, if G is solvable and the field Q ( χ ) generated by the values of χ over Q satisfies | Q ( χ ) : Q | ⩽ k , for all χ ∈ Irr ( G ) , then the set of prime divisors of | G | is bounded in terms of k . Also, we prove that the degree of the field generated by the values of all characters of a semi-rational solvable group (see Chillag and Dolfi, 2010 [1] ) or a quadratic rational solvable group over Q is bou…