• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.847-868
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• 2016

Let M be an invariant subspace of $H^2$ over the bidisk. Associated with M, we have the fringe operator $F^M_z$ on $M{\ominus}{\omega}M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces M. Also ker $F^M_z$ and ker $(F^M_z)^*$ are described.

• Journal of Mechanical Science and Technology
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• v.16 no.2
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• pp.175-181
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• 2002

A new polariscope system involving two rotating optical elements and a digital camera for whole field fringe analysis allows automated data to be acquired quickly and efficiently. The developed phase measuring technique that uses eight images through a circular polariscope is presented for the digital measurement of isochromatics and isoclinics, respectively, from photoelastic fringes in a circular disk under diametric compression. Isochromatics can directly be obtained using wrapped isoclinic phases calculated by the arc tangent operator which is the four-quadrant operator from -$\pi$ to $\pi$. It is not required to unwrap isoclinic phases for the calculations of isochromatics. Unwrapped isoclinics are directly determined from isochromatic parameters. Distributions of digitally determined isoclinics are in close agreement to manual measurements. The errors which would appear in unwrapping process of isoclinics can be avoided in the determination of isochromatics.