• Bulletin of the Korean Chemical Society
• /
• v.21 no.12
• /
• pp.1227-1232
• /
• 2000

Near the conical intersection for the 1,2 $^{2}A'$ states of $H_3$ the derivative coupling vector is calculated and analyzed on the plane of internal coordinates, (U,V) or its polar coordinates $(S{\theta})$, based on the squares of the internuclear distances. It is shown that in the vicinity of the conical intersection the derivative coupling vector behaves like ${\theta}/2S$, which is responsible for the sign changes of the real-valued electronic wave function when the nuclear configuration traverses a closed path enclosing a conical intersection. The analytic property of the wave functions is studied and especially the observation of the sign change in the configuration state function (CSF) coefficients of the real-valued electronic wave functions is demonstrated.

• Steel and Composite Structures
• /
• v.38 no.4
• /
• pp.447-462
• /
• 2021

In this work, we consider a problem in the context of thermoelectric materials with memory-dependent derivative for a half space which is assumed to have variable thermal conductivity depending on the temperature. The Lamé's modulii of the half space material is taken as a function of the vertical distance from the surface of the medium. The surface is traction free and subjected to a time dependent thermal shock. The problem was solved by using the Laplace transform method together with the perturbation technique. The obtained results are discussed and compared with the solution when Lamé's modulii are constants. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions. Affectability investigation is performed to explore the thermal impacts of a kernel function and a time-delay parameter that are characteristic of memory dependent derivative heat transfer in the behavior of tissue temperature. The correlations are made with the results obtained in the case of the absence of memory-dependent derivative parameters.

• East Asian mathematical journal
• /
• v.21 no.1
• /
• pp.123-135
• /
• 2005

We have extended the $H^p$ space and estabilished the derivative of inner functions, Blaschke product on weighted Hardy spaces for the unit disc in complex plane.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.1
• /
• pp.159-164
• /
• 2017

This paper deals with linear impulsive differential equations involving the Caputo fractional derivative. We provide exact solutions of nonhomogeneous linear impulsive fractional differential equations with constant coefficients by means of the Mittag-Leffler functions.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.119-122
• /
• 1988

In recent years, several authors have dealt with the fraction derivative [1], in special functions [2], convolution integral equation [5], differintegral equation [4], the derivative of H-function [6], and some other applications. The present paper considers the fraction derivatve in the form of differential eqiation.

• Journal of Soil and Groundwater Environment
• /
• v.15 no.6
• /
• pp.46-52
• /
• 2010

Derivative analysis, based on the derivative of the drawdown as a function of time (i.e., rate of drawdown change), was applied to the evaluation of hydraulic parameters of the aquifer as an aid of the aquifer test interpretation based on the Theis solutions. Pumping tests were conducted at a coastal fractured aquifer in Muan county, Korea, of which the drawdown data, measured at the two observation wells, were used for derivative analysis. Wellbore storage and transition period were hard to identify at conventional log-log and semi long plots, but was easily recognized by distinctive curves of positive unit slope, hump and negative unit slope in the derivative plot. For the observation well of OW-2 at which wellbore storage and transition lasted over an hour, conventional aquifer analysis would suffer from the uniqueness problems and in further result in erroneous hydraulic parameters. Derivative analysis was found to be effective for distinguishing the drawdown data directly reflecting the aquifer property from those reflecting non aquifer effects such as wellbore storage and transition, which offers a unified methodology to yield correct hydraulic parameters from aquifer test data.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.299-306
• /
• 2006

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The 'Hamilton-Jacobi (H-J)' equation and computationally robust numerical technique of 'up-wind scheme' lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H -J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes is not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• Journal of Magnetics
• /
• v.22 no.1
• /
• pp.43-48
• /
• 2017

In order to detect the current flowing through concealed conductor, this paper proposes a new method based on derivative method. Firstly, this paper analyzes the main peak characteristic of the derivative function of magnetic field generated by a current-carrying conductor, and a relationship between the current flowing through the conductor and the main peak of the derivative function is obtained and applied to calculate the current. Then, the method is applied to detect the conductor current flowing through grounding grids of substations. Finally, the numerical experimental and field experiment verified the feasibility and accuracy of the method, and the computing results show that the method can effectively measure the conductor current of grounding grids with low error, and the error is within 5 %.

• Kyungpook Mathematical Journal
• /
• v.60 no.3
• /
• pp.507-518
• /
• 2020

We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by 𝒩. For the function f(z) = z + a₂z² + a₃z³ + … which is defined in the unit disc D such that the function f(z) belongs to the class 𝒩, we estimate from below the modulus of the angular derivative of the function ${\frac{f{^{\prime}^{\prime}}(z)}{f(z)}}$ at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.

• The Pure and Applied Mathematics
• /
• v.26 no.2
• /
• pp.59-73
• /
• 2019

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to $\mathcal{N}$(${\alpha}$) is investigated. For the function $f(z)=z+c_2z^2+C_3z^3+{\cdots}$ which is defined in the unit disc where $f(z){\in}\mathcal{N}({\alpha})$, we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with $f(b)={\frac{1}{b}}\int\limits_0^b$ f(t)dt. The sharpness of these inequalities is also proved.