• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.549-554
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• 2014

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[${\omega}_i$]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K$\ddot{a}$hler metrics in [5], satisfies $Z(M,[[{\omega}_1]])={\infty}$ and $Z(M,[[{\omega}_2]])$ < 0.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.93-105
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• 2018

There are many metric functions in the plane. In this paper we are to classify the metric functions on the plane using two ways such as using sum of distances between some points when start point and end point is fixed, and using area of transferred triangle consisted of distances between 3 points.

• Journal of Pharmaceutical Investigation
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• v.33 no.3
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• pp.245-253
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• 2003

Dissolution profile comparsions can be done by virtue of the similarity factor $(f_2)$. It is a logarithmic reciprocal square root transformation of the sum of squared error of % dissolution differences between two profiles at several time points. It gives information on the degree of similarity between the two profiles: An $f_2$ value between 50 and 100 suggests the similarity/equivalence of the two dissolution curves being compared. The objective of this report was to provide a careful examination on the $f_2$ metrics in detail. It was shown that $f_2$ values exceeded 50, when relative differences in % dissolved between two products were less than 15% at all time points. The similarity factor value was also found to be greater than 50, in cases when absolute % dissolution differences were below 10% at all time points. Interestingly, the $f_2$ value was changed by the number of the time points selected for calculation. In particular, $f_2$ tended to have higher values, when the $f_2$ metrics used a large number of time points in which % dissolved reached plateau. Finally, since the similarity factor was a sample statistics, it was impossible to infer type I/II errors and sampling error. Despite certain limitations inherited in the $f_2$ metrics, it was easy and convenient to evaluate how similar the two dissolution profiles were.