We consider the quadratic eigenvalue problem (QEP) (λ2M + λG + K)x = 0, where M = MT is positive definite, K = KT is negative definite, and G = −GT . The eigenvalues of the QEP occur in quadruplets (λ, λ,−λ,−λ) or in real or purely imaginary pairs (λ,−λ). We show that all eigenvalues of the QEP can be found efficiently and with the correct symmetry, by finding a proper solvent X of the matrix e...

The quantitative errors of extinction efficiency during the particulate measurement caused by the refractive index are studied. And the quantitative results are acquired when the real part of the refractive index and the imaginary part change respectively. The change ranges of the real part are 1+0.5 i to 2+0.5 i at a 0.1 interval and 1.5+0.5 i to 1.59+0.5 i at a 0.01 interval. Another the chan...

The imagination and creativity of children is often puzzling to the adult mind. Pretend play and make-believe friends are often prevalent in the life of a child. Past research shows a relationship between the use of the imagination in children’s play and their social, cognitive, and emotional development. Furthermore, there are a number of gender differences in the type of imaginary play and pr...

Dyna planning is an efficient way of learning from real and imaginary experience. Existing tabular and linear Dyna algorithms are single-step, because an “imaginary” feature is predicted only one step into the future. In this paper, we introduce a multi-step Dyna planning that predicts more steps into the future. Multi-step Dyna is able to figure out a sequence of multi-step results when a real...

Using the exactly solvable Gross-Neveu model as theoretical laboratory, we analyse in detail the relationship between a relativistic quantum field theory at real and imaginary chemical potential. We find that one can retrieve the full information about the phase diagram of the theory from an imaginary chemical potential calculation. The prerequisite is to evaluate and analytically continue the ...