• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.515-522
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• 1997

In this paper, we find the second derivative of mean busy cycle with respect to a parameter of inter-arrival time distribution. We show that this derivative can be estimated from single sample path. We do the similar thing for the mean number of arrivals during busy cycle.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.913-921
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• 2010

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.335-344
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• 2015

In the paper we discuss the value distribution of the product of the derivative of a transcendental meromorphic function and a power of the function.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.387-396
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• 2017

Our aim is to study covariant derivative with respect to complete and vertical lifts of generalized almost r-contact structure in tangent bundle.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.865-875
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• 2020

We provide detailed proofs for local gradient estimates for weak solutions to elliptic equations in divergence form with partial Dini mean oscillation coefficients subject to conormal derivative boundary conditions.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.287-294
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• 2023

The goal of this paper is to extend some inequalities of Bernstein as well as Turán type to polar derivative of a polynomial.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.49-54
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• 2023

In this paper, we obtain some results concerning the location of zeros of generalized derivatives of polynomials which are analogous to those for the ordinary derivative of polynomials.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.251-278
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• 2008

In this study, we investigate the discontinuous-derivative treatment at the gas-liquid interface in underwater explosion (UNDEX) problems by using the Moving Least Squares-Smoothed Particle Hydrodynamics (MLS-SPH) method, which is known as one of the particle methods suitable for problems where large deformation and inhomogeneity occur in the whole domain. Because the numerical oscillation of pressure arises from derivative discontinuity in the UNDEX analysis using the standard SPH method, the MLS shape function with Discontinuous-derivative Basis Function (DBF) that is able to represent the derivative discontinuity of field function is utilized in the MLS-SPH formulation in order to suppress the nonphysical pressure oscillation. The effectiveness of the MLS-SPH with DBF is demonstrated in comparison with the standard SPH and conventional MLS-SPH though a shock tube problem and benchmark standard problems of UNDEX of a trinitrotoluene (TNT) charge.

• School Mathematics
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• v.12 no.2
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• pp.239-257
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• 2010

In school mathematics the derivative concept is intuitively taught with the tangents and the concept of instantaneous velocity. In this paper, I investigated the long historical developments of the derivative concepts and analysed the relationships between the definition of derivative and the related elements. Finally I proposed some educational implications based on the analysis.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.2
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• pp.175-185
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• 2017

This paper presents new differential methods for computing the combined and single dynamic stability derivatives of flight vehicle. Based on rigid dynamic mesh technique, the combined dynamic stability derivative can be achieved by imposing the aircraft pitching to the same angle of attack with two different pitching angular velocities and also translating it to the same additional angle of attack with two different rates of angle of attack. As a result, the acceleration derivative is identified. Moreover, the rotating reference frame is adopted to calculate the rotary derivatives when simulating the steady pull-up with different pitching angular velocities. Two configurations, the Hyper Ballistic Shape (HBS) and Finner missile model, are considered as evaluations and results of all the cases agree well with reference or experiment data. Compared to traditional ones, the new differential methods are of high efficiency and accuracy, and potential to be extended to the simulation of combined and single stability derivatives of directional and lateral.