• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1145-1166
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• 2022

In this paper, for a transcendental meromorphic function f and α ∈ ℂ, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: $$f^n+{\alpha}f^{n-2}f^{\prime}+P_d(z,f)={\sum\limits_{i=1}^{k}}{p_i(z)e^{{\alpha}_i(z)},$$ where P_d(z, f) is a differential polynomial of f, p_i's and α_i's are non-vanishing rational functions and non-constant polynomials, respectively. When α = 0, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case α ≠ 0 has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.29-36
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• 2003

In 1970 Monsky proved that a square cannot be cut into an odd number of triangles of equal areas. In 1990 it was proved that the statement is true for any centrally symmetric polygon. In the present paper we consider dissections of general polygons into triangles of equal areas.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.311-319
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• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.797-807
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• 2019

In this study, an exact transfer matrix expression for a twisted uniform beam considering the effect of shear deformation and rotary inertia is developed. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. The results obtained from this method are independent for a number of subdivided elements, and this method can determine the required number of exact solutions for the free vibration characteristics of a twisted uniform Timoshenko beam using a single element. In addition, it can be used as a useful numerical method for the computation of high-order natural frequencies. To validate the accuracy of the proposed method, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of shear deformation and rotary inertia for a twisted beam.

• Journal of Power Electronics
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• v.15 no.4
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• pp.964-973
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• 2015

This paper presents a simple approach for the selective harmonic elimination (SHE) of multilevel inverter based on the transistor-clamped H-bridge (TCHB) family. The SHE modulation is derived from the sinusoidal voltage-angle equal criteria corresponding to the optimized switching angles. The switching angles are computed offline by solving transcendental non-linear equations characterizing the harmonic contents using the Newton-Raphson method to produce an optimum stepped output. Simulation and experimental tests are conducted for verification of the analytical solutions. An Altera DE2 field-programmable gate array (FPGA) board is used as the digital controller device in order to verify the proposed SHE modulation in real-time applications. An analysis of the voltage total harmonic distortion (THD) has been obtained for multiple output voltage cases. In terms of the THD, the results showed that the higher the number of output levels, the lower the THD due to an increase number of harmonic orders being eliminated.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.319-339
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• 2010

In this paper, we prove that if $f^nf'\;-\;P$ and $g^ng'\;-\;P$ share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.14 no.2
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• pp.138-149
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• 1985

The heat diffusion equation for an annular fin is analyzed using Laplace transformations. The fin has a uniform thickness with its edge heat loss and two temperature profiles at the base such as a step change in temperature or heat flux. To obtain the exact solutions for temperature distribution, this paper can detect the eigenvalues which satisfy the roots of transcendental equations in above two cases during inverse Laplace transformations. The exact solutions for temperature and heat flux are obtained with the infinite Series by dimensionless factors. The solutions are developed for small and large values of times. These series solutions converge rapidly for large values of time, but slowly for small.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.217-224
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• 2016

In this study, a transfer matrix method (TMM) for a twisted uniform beam considering the effect of rotary inertia is developed, and the differential equation and the displacements and forces are derived from Hamilton's principle. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. In addition, the results obtained from this method are independent for a number of subdivided elements, and this method can determine the exact solutions for the free vibration characteristics of a twisted uniform Rayleigh beam. To validate the accuracy of the proposed TMM, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of rotary inertia for a twisted beam.

• Journal of Korean Academy of Nursing
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• v.34 no.5
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• pp.673-684
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• 2004

Purpose: The purpose of the study was to meta-analyze the relationships of major concepts, which were made by synthesizing similar explanatory variables into more comprehensive concepts, to hope. Method: The relevant researches from Jan 1980 to Dec 2003, performed in adults or adult patients, were collected. Using the SAS program, meta-analysis were done with the input data of the number of subjects, the correlation coefficients provided from most of the studies or a few transformed correlation coefficients from F value. In order to get the analysis to be done in homogeneous status of the data regarding each relationship of each major concept to hope(p> 0.05), heterogeneous data were eliminated in repeating Q-test. Result: The major variable regarding relationship to self/transcendental being/life(spiritual wellbeing & self esteem) and social support(social support & family support) have very large positive effects on hope(D=l.72, D=l.27). The negative effect of the variable regarding captive state(uncertainty in illness, perceived unhealthiness status, & fatigue) and positive effect of coping(approach coping) on hope are in the level between moderate to large(D=-0.61, D=0.78). All the effects of the major concepts on hope were verified as significant statistically(p=.000). The Fail -Safe numbers showed the significant effects of the three major concepts except coping on hope were reliable. Conclusion: The results can be a guide to advance hope theory for nursing.

• Journal of Power Electronics
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• v.16 no.2
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• pp.512-521
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• 2016

Cascaded H-bridge multilevel (CHBML) inverters usually include a large number of isolated dc-voltage sources. Some faults in the dc-voltage sources result in unequal cell dc voltages. Unfortunately, the conventional phase-shifted carrier (PSC) PWM method that is widely used for CHBML inverters cannot eliminate low frequency sideband harmonics when the cell dc voltages are not equal. This paper analyzes the principle of sideband harmonic elimination, and proposes an improved PSCPWM that can eliminate low frequency sideband harmonics under the condition of unequal dc voltages. In order to calculate the carrier phases, it is necessary to solve transcendental equations for low frequency sideband harmonic elimination. Therefore, an approach based on the artificial bee colony (ABC) algorithm is presented in this paper. The proposed PSCPWM method enhances the reliability of CHBML inverters. The proposed PSCPWM is not limited to CHBML inverters. It can also be applied to other types of multilevel inverters. Simulation and experimental result obtained from a prototype CHBML inverter verify the theoretical analysis and the achievements made in this paper.