• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.687-696
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• 2023

In this paper, we introduce the 2-variable mixed-type Hermite polynomials and organize some new symmetric identities for these polynomials. We find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.869-882
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• 2023

In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.315-331
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• 2015

The purpose of this paper is to obtain Opial-type inequalities that are useful to study various qualitative properties of certain differential equations involving impulses. After we obtain some Opial-type inequalities, we apply our results to certain differential equations involving impulses.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.433-434
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• 2006

The limited slip differential(LSD) is a device which enables the driving force to be transmitted from one slipping wheel to another wheel in such case that the car is stuck in clay or snow. When the unwanted slipping occurs on one wheel, the LSD temporarily restraints the differential motion to transmit the driving force in the other wheel. So far, many types of LSD were developed such as mechanical lock type, disk clutch type, viscous coupling type, torsion type and multiple clutch type. we designed a new type of the hydraulic LSD which uses the principle of trochoid gear pump.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.49-63
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• 2009

We obtain some retarded integral inequalities of Bihari-type and apply these results to a retarded differential equation of Bernoulli-type.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.141-150
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• 2000

Continuously variable transmission(CVT) combined differential gear unit has many advantages, which are the decrease of CVT size, the increase of overall efficiency, the extension of speed ratio range, and the generation of geared neutral. It is known that such CVT can be classified into the input coupled type and the output coupled type according to the coupling location of continuously variable unit(CVU). In this paper, six different configurations of input coupled type CVT combined V-belt CVU and 2K-H I type differential gear unit are proposed. Some useful theoretical formula related to speed ratio, power flow and efficiency are derived and analyzed. The propriety of derived formula and theoretical analysis are proven by various experiments.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.465-483
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• 2021

Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓_j)ⁿ_j=0 and 𝚽 = (𝚽_j)ⁿ_j=0 be such that 𝜓_j, 𝚽_j ∈ 𝓗(𝔻). The linear differential operator is defined by T_𝜓(f) = ∑ⁿ_j=0 𝜓_jf^(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T_𝜓 - T_𝚽)(f) = ∑ⁿ_j=0 (𝜓_j - 𝚽_j) f^(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.447-456
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• 2015

In this paper, we investigate the differential-difference equation $(f(z+c)-f(z))^2+P(z)^2(f^{(k)}(z))^2=Q(z)$, where P(z), Q(z) are nonzero polynomials. In addition, we also investigate Fermat type q-difference differential equations $f(qz)^2+(f^{(k)}(z))^2=1$ and $(f(qz)-f(z))^2+(f^{(k)}(z))^2=1$. If the above equations admit a transcendental entire solution of finite order, then we can obtain the precise expression of the solution.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.83-99
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• 2022

In this paper, we extend some previous works by Liu et al. on the existence of transcendental entire solutions of differential-difference equations of Fermat type. In addition, we also present a precise description of the associated entire solutions.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.226-233
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• 1999

Protective relay for transformer operates in general by comparing with the differential current and the restraint current. These kinds of currents are changed on magnitude and phasor during the fault according to winding type and vector group. This paper presents the differential and restraint currents and operational principle of differential protective relay for two-winding and three-winding transformer with graphical mode. It is developed using MATLAB for and educational purpose on engineer related in power system and protection in university and power utility including large factory.