• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.8
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• pp.1193-1198
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• 2012

An instantaneous amplitude (IA) estimator using the symmetric higher order differential energy operator is proposed. The amplitude estimator and the instantaneous frequency (IF) estimator based on the symmetric higher order differential energy operator coincide with the analyzed signal in time, and they show better estimation results than the IA and IF based on the higher order differential energy operator. Various IF and IA estimators are applied to AM-FM signals for the performance comparison. Among the IF and IA estimators, the IF and IA estimators based on the symmetric higher order energy operator show the best estimation accuracy. Then, the IA and IF estimators are applied to the distorted power line signal to show their usefulness as power disturbance detectors.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.903-917
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• 2023

This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

• East Asian mathematical journal
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• v.14 no.2
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• pp.299-309
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• 1998

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.223-233
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• 2010

In this paper, we use q-differential operator to recover the finite Heine $_2\Phi_1$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.73-76
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• 1998

It is proved that the partial differential operator $D_x + ix^q D^2_y$ is not locally solvable in any open set which intersects the line x = 0, when $q = - \frac{2l-1}{2k-1}$ is not an integer.

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

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.105-115
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• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.503-519
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• 2015

In this work, certain classes of admissible functions are considered. Some strong dierential subordination and superordination properties of analytic functions associated with new generalized derivative operator $B^{{\mu},q,s}_{{\lambda}_1,{\lambda}_2,{\ell},d}$ are investigated. New strong dierential sandwich-type results associated with the generalized derivative operator are also given.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.47-55
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• 2009

In the present investigation sufficient conditions are found for certain subclass of normalized analytic functions defined by Hadamard product. Differential sandwich theorems are also obtained. As a special case of this we obtain results involving Ruscheweyh derivative, S$\u{a}$l$\u{a}$gean derivative, Carlson-shaffer operator, Dziok-Srivatsava linear operator, Multiplier transformation.