• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.1-15
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• 2010

We introduce, in this article, the quasi-stable exchange ideal for associative rings. If I is a quasi-stable exchange ideal of a ring R, then so is $M_n$(I) as an ideal of $M_n$(R). As an application, we prove that every square regular matrix over quasi-stable exchange ideal admits a diagonal reduction by quasi invertible matrices. Examples of such ideals are given as well.

• Proceedings of the Korea Crystallographic Association Conference
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• 2002.11a
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• pp.18-18
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• 2002

Although it was suggested in 1962 that an efficient wavelength conversion could be achieved using ferroelectric crystals of periodic 180° domains, it was not until 1990's that quasi-phase-matching (QPM) became realized, as technology for periodic poling of LiNbO₃ crystals was readily available. Since ferroelectric domain inversion brings about change of the sign of second-order nonlinear susceptibility, periodically poled ferroelectric structures provide an ideal way of achieving QPM for second-harmonic generation and optical parametric oscillation. Periodically poled ferroelectric domains can also be utilized for optical devices, such as Brags electrooptic modulators. fabrication of stable periodic domain structures depends on a number of poling parameters of a ferroelectric crystal, such as coercive field, internal field and electrical conductivity. We present poling kinetics of KNbO₃ crystals, which involve domain nucleation and growth, backswitching, relaxation of internal field. Optimum poling conditions were established by designing a proper wave shape of external field. We demonstrate an efficient second-harmonic generation using QPM in a periodically poled KNbO₃ crystal.