• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.147-154
• /
• 2009

Tamanoi proposed higher Schwarzian operators which include the classical Schwarzian derivative as the first nontrivial operator. In view of the relations between the classical Schwarzian derivative and the analogous differential operator defined in terms of Peschl's differential operators, we define the generating function of our generalized higher operators in terms of Peschl's differential operators and obtain recursion formulas for them. Our generalized higher operators include the analogous differential operator to the classical Schwarzian derivative. A special case of our generalized higher Schwarzian operators turns out to be the Tamanoi's operators as expected.

• Journal of electromagnetic engineering and science
• /
• v.11 no.1
• /
• pp.56-61
• /
• 2011

In this paper, we consider the topological derivative concept for developing a fast imaging algorithm of thin inclusions with dielectric contrast with respect to an embedding homogeneous domain with a smooth boundary. The topological derivative is evaluated by applying asymptotic expansion formulas in the presence of small, perfectly conducting cracks. Through the careful derivation, we can design a one-iteration imaging algorithm by solving an adjoint problem. Numerical experiments verify that this algorithm is fast, effective, and stable.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1391-1409
• /
• 2016

In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.

• Honam Mathematical Journal
• /
• v.41 no.1
• /
• pp.153-161
• /
• 2019

In practical applications play an new important role timelike biharmonic particle by Fermi-Walker derivative. In this article, we get a innovative interpretation about timelike biharmonic particle by means of Fermi-Walker derivative and parallelism in Heisenberg spacetime. With this new representation, we derive necessary and sufficient condition of the given particle to be the inextensible flow. Moreover, we provide several characterizations designed for this particles in Heisenberg spacetime.

• Honam Mathematical Journal
• /
• v.41 no.2
• /
• pp.381-390
• /
• 2019

In this paper, we introduce interesting subclasses ${\mathcal{H}}^{p,q,{\beta},{\alpha}}_{{\sigma}B}$ and ${\mathcal{H}}^{p,q,{\beta}}_{{\sigma}B}({\gamma})$ of bi-univalent functions by (p, q)-derivative operator. Furthermore, we find upper bounds for the second and third coefficients for functions in these subclasses. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.507-522
• /
• 2019

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.631-638
• /
• 2021

In this paper, some sharp inequalities for ordinary derivative P'(z) and polar derivative D_αP(z) = nP(z) + (α - z)P'(z) are obtained by including some of the coefficients and modulus of each individual zero of a polynomial P(z) of degree n not vanishing in the region |z| > k, k ≥ 1. Our results also improve the bounds of Turán's and Aziz's inequalities.

• Honam Mathematical Journal
• /
• v.42 no.4
• /
• pp.769-780
• /
• 2020

In this paper, Fermi-Walker derivative for inextensible flows of curves are researched in 3-dimensional Galilean space G3. Firstly using Frenet and Darboux frame with the help of Fermi-Walker derivative a new approach for these flows are expressed, then some results are obtained for these flows to be Fermi-Walker transported in G3.

• The Journal of Korean Medicine
• /
• v.23 no.2
• /
• pp.39-56
• /
• 2002

Objective : The aim of this study is to investigate the inhibitory effect of lnjinchunggantang-derivative on acute and sub-acute hepatic fibrosis induced by $CCl_4$, and to compare the efficiency of lnjinchunggantang-derivative, Salviae Radix and Scirpi Tuber.Zeloariae Rhizoma on acute and sub-acute hepatic fibrosis induced by $CCl_4$. Method : Western blotting for collagen type N, quantitative RT-PCR and gross & histological findings on liver tissue (Hematoxylin & Eosin stain, Reticulin stain, Masson-Trichrome stain) were studied. Results : In the study on collagen type N expression, lnjinchunggantangcderivative, Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix showed inhibitory effect in western blotting. In quantitative RT-PCR assay, lnjinchunggantang-derivative showed inhibitory effect on collagen type N expression in acute hepatic fibrosis model, whereas lnjinchunggantang-derivative, Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix showed inhibitory effect on collagen type N expression in sub-acute hepatic fibrosis model. In the gross findings of acute and sub-acute hepatic fibrosis models,lnjinchunggantang-derivative, Salviae Radix and Scirpi Tuber. Zeloariae Rhizoma showed inhibitory effect on hepatic fibrosis in the order. In the histological findings of acute and sub-acute hepatic fibrosis models in Hematoxylin & Eosin, Reticulin and Masson-Trichrome staining, the liver of $CCl_4$-only group showed atrophy and necrotic change with white nodules whereas that of $CCl_4$+ Injinchunggantang-derivative showed no significant histological change with well preservation of the tone of the tissue, and Scirpi Tuber. Zeloariae Rhizoma and Salviae Radix group showed minimal fibrotic changes. In the scoring system of the extent of the inhibition of the hepatic fibrosis, lnjinchunggantang-derivative group showed statistically significant inhibitory effect(p<0.05) whereas Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix group showed no statistically significant effect in the acute hepatic fibrosis model. In the sub-acute hepatic fibrosis model, lnjinchunggantang-derivative, Scirpi Tuber.Zeloariae Rhizoma and Salviae Radix group showed statistically significant effect (p<0.01). Conclusion : These results show that lnjinchunggantang-derivative, Salviae Radix and Scirpi Tuber.Zeloariae Rhizoma have inhibitory effect in the order on hepatic fibrosis induced by $CCl_4$ by suppressing the expression of collagen type N, ultimately preventing liver cirrhosis. To obtain more credible results in this experiment, developement of a new experimental model more similar to human hepatic fibrosis is still needed.

• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.559-567
• /
• 2015

This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.