• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.913-927
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• 2024

In this paper, we represent regular functions on ternary theory in the view of quaternion. By expressing quaternions using ternary number theory, a new form of regular function, called E-regular, is defined. From the defined regular function, we investigate the properties of the appropriate hyper-conjugate harmonic functions and corresponding Cauchy-Riemann equations by pseudo-complex forms.

• Structural Engineering and Mechanics
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• v.44 no.5
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• pp.681-704
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• 2012

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

• Journal of Power Electronics
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• v.12 no.6
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• pp.935-946
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• 2012

A new kind of resonant impedance type hybrid active filter (RITHAF) is proposed for dynamic harmonic current suppression and high capacity reactive compensation in medium and high voltage systems. This paper analyzed the different performance of the RITHAF when the active part of the RITHAF is controlled as a current source and as a voltage source, respectively. The harmonic suppression function is defined in this paper. The influences of the changes caused by the grid impedance and the detuning of the passive power filter on the compensating characteristics of the RITHAF are studied by analyzing the suppression function. Simulation and industrial application results show that the RITHAF has excellent performances in harmonic suppression and reactive compensation, which is suitable for medium and high voltage systems.

• Bulletin of the Korean Chemical Society
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• v.23 no.2
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• pp.355-356
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• 2002

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1277-1288
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• 2013

Wulan and Zhu [16] have characterized the weighted Bergman space in the setting of the unit ball of $C^n$ in terms of Lipschitz type conditions in three different metrics. In this paper, we study characterizations of the harmonic Bergman space on the upper half-space in $R^n$. Furthermore, we extend harmonic analogues in the setting of the unit ball to the full range 0 < p < ${\infty}$. In addition, we provide the application of characterizations to showing the boundedness of a mapping defined by a difference quotient of harmonic function.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.771-776
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• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.13-36
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• 2018

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.819-835
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• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.85-91
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• 2003

On the setting of the upper half-space of the euclidean space $\mathbf{R}^n$, we show some properties of weighted harmonic Bergman functions.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.553-574
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• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.