Irregularities of microhyperbolic operators

Irregularities of semilinear hyperbolic equations

“…For this equation the situation is the same as in Example 1.3 (see [7,8,9,13,18,21]). This is called non-involutive in linear theory, and timely degenerate in nonlinear theory.…”

“…. }, and [18,21]. It is called a spatially degenerate equation in nonlinear theory, and recently many people are studying it.…”

“…This result was generalized by [5] to nonlinear equations with constant multiplicities. Our irregularity was defined by [21] for a linear microhyperbolic operator. We call the above representation (2.1) a Lascar decomposition, because R. Lascar considered such a representation in [16] to study linear regularly involutive operators.…”

Formation of Composite Coatings of Layered Double Hydroxide Particles and Hydroxide Gel by Electrophoretic Deposition on Mg Alloy and Corrosion Resistance

“…It was reported that the zeta potential of alumina particles increased in the positive direction with a decrease in pH of the EPD suspension. 19) In this study, the pH of the EPD suspensions measured by a glass electrode pH meter was 8.3, 7.0 and 5.8 for the suspensions with 1.25, 12.5 The cross-section SEM images (Fig. 2) showed that gelrich layers (indicated by white arrow heads) and particle-rich layers (indicated by white arrows) almost alternately piled up in the composite layers which thickened with an increase of Mg and Al ions from sub-micrometers to about 30 µm.…”