• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.169-181
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• 2007

Applying the properties of Hadamard core for totally nonnegative matrices, we give new lower bounds of the determinant for Hadamard product about matrices in Hadamard core and totally nonnegative matrices, the results improve Oppenheim inequality for tridiagonal oscillating matrices obtained by T. L. Markham.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.317-333
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• 2024

For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S^*_s(𝜑) and C_s(𝜑), respectively, the sharp bound of the n^th Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

• Journal of Life Science
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• v.14 no.5
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• pp.770-777
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• 2004

It has been previously reported that unacetylated a-tropomyosin(TM) produced in E. coli failed to bind to actin while acetylated muscle TM and Ala-Ser dipeptide fusion TM (AS-TM) bound well to actin. In order to determine the structural requirement of the amino terminus for high actin affinity, a recombinant tropomyosin (Ala-TM) that a single Ala residue was added to the amino terminus of Ala-TM was constructed, overexpressed, and purified from E. coli. Actin affinity of Ala-TM was 2.3$\times$$10^{6}$$M^{-1}$, whereas that of unacetylated TM was considerably lower than 0.1$\times$$10^{-6}$$M^{-1}$ indicating that addition of a single Ala residue to the amino terminus drastically increased, at least twenty times, actin affinity of TM. Ala-TM, however, bound to actin about three times weaker than acetylated TM and AS- TM, implying that the addition of an Ala residue was insufficient for complete restoration of high actin affinity. While Ala-TM, AS-TM, and muscle TM showed inhibition and activation of actomyosin Sl ATPase activity depending on myosin Sl concentration, the degree of inhibition and activation was different from each other. AS-TM exhibited the greatest inhibition of the ATPase at low Sl concentration, whereas the greatest activation of the ATPase was observed with muscle TM. These results, together with previous findings, strongly suggested that local structure of the amino terminus is the crucial functional determinant of TM.