• Honam Mathematical Journal
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• v.34 no.3
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• pp.327-340
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• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Very recently, Choi defined a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}^2_n({\cdot})$ and presented their several generating functions. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in m variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, in the sequel of the above results for their possible general $q$-extensions in several variables, again, we aim at trying to define a $q$-extension of the generalized three variable Gottlieb polynomials ${\varphi}^3_n({\cdot})$ and present their several generating functions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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• pp.2023-2032
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• 1993

This study suggests a new type shaft generating system driven by hydrostatic transmission suitable for small size vessels. Since the shaft generating system is affected ceaselessly by disturbances such as speed variation in pump driving speed and variation in external load, a robust servo control must be implemented to obtain stable electric power with constant frequency. Thus, in this study, a digital robust servo control algorithm is applied to the controller design. By the experiment and the numerical computation, the frequency variation characteristics of the generating system under various disturbances are investigated. Conclusively, it is said that the shaft generating system proposed in this study shows excellent control performances.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.473-484
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• 2018

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.783-797
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• 2013

Recently, Liu et al. [Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella function, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549] investigated, in several interesting papers, some various families of bilateral generating functions involving the Chan-Chyan-Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Chan-Chyan-Sriavastava polynomials and three general classes of multivariable polynomials introduced earlier by Srivastava in [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6], [A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191] and by Kaano$\breve{g}$lu and $\ddot{O}$zarslan in [Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631]. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.265-284
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• 2019

The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1277-1292
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• 2009

This paper is an attempt to stress the usefulness of the multivariable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.3
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• pp.69-75
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• 1983

This paper presents a improved algorithm for the generating capacity reliability evaluation using the frequency and duration approach. One of the specific feature of this algorithm is that propose the cumulative state load model via analytic expression of load duration curve and cumulative load frequency characteristic in conside ration of daily peak load. The paper illustrates the utilization of the proposed algorithm in actual system studies using the generating system of KEPCO. The results presented will provide a valuable reference for maintaining and planing the generating system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.661-666
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• 2000

Traveling wave on the structure can be generated by superposing two standing waves. Precise matching of the amplitudes and phase shift between two standing waves in time and space is the key to the success of generating a traveling wave. The principle of generating a traveling wave on the structure is utilized in the construction of linear and rotary type ultrasonic motors. This paper demonstrates experimentally generating a traveling wave on the simply supported beam.

• Journal of the Korean Chemical Society
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• v.54 no.5
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• pp.621-632
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• 2010

In this study, we examined the characteristics of analogies generated by science-gifted students depending on the consideration of attributes and relationships in the processes of generating analogies and investigated the applicability of analogy-generating activities in science-gifted education programs. The analyses of the results revealed that the analogy-generating processes of science-gifted students were categorized into three kinds of patterns depending on the consideration of attributes and relationships of the target concept and the source analog. There are also some differences in the types of analogies generated and selected to be good, and in the proper mapping numbers by the patterns depending on the consideration of attributes and relationships. Most science-gifted students used the analogy-generating activities to other target concept, and recognized them to be useful. However, they had difficulties in selecting source analogs at the processes of generating analogy. These obtained in this study will help to explore a potential use of the analogy-generating activities in an effective education program for fostering the creativity of science-gifted students.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1873-1882
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• 2017

We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of q-partite graphs of given order, size and number of connected components.