• 대한수학회논문집
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• 제13권1호
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• pp.73-76
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• 1998

It is proved that the partial differential operator $D_x + ix^q D^2_y$ is not locally solvable in any open set which intersects the line x = 0, when $q = - \frac{2l-1}{2k-1}$ is not an integer.

• 전기학회논문지
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• 제59권10호
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• pp.1889-1893
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• 2010

Differential pressure type level measuring systems have been using widely for industrial applications like drum level measurements in power plants. Because of difficulties in specific gravity compensation for vapor and liquid inside the vessel and the sensing lines, this type of measuring systems reveal significant measuring error. In this paper, the major reason causing errors on the differential pressure type level measurement is analyzed and a method of more accurate calculation for specific gravity compensation is introduced.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.147-154
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• 2013

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

• 한국정밀공학회지
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• 제21권4호
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• pp.170-178
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• 2004

Continuously variable transmission (CVT) mechanisms considered here are input coupled types that combine the functions of a 2K-H II type differential gear and a V-belt type continuously variable unit (CVU). For the 8 different mechanisms, 4 of them are power-circulation modes while the other 4 are power-split modes, various performance analysis (speed ratios, power flows, divisions of power transmission in a differential gear and a CVU, and theoretical efficiencies) are performed to vary design parameters. Experimental studies are executed to validate fundamental relations (speed ratios, power flows, efficiencies, occurrence of geared neutral). Some useful characteristics associated with performance also are discussed in the mechanisms.

• 전기의세계
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• 제14권6호
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• pp.1-7
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• 1965

This paper provides the analysis of the differential amplifier using the insulated gate, metala-oxide-semiconductor type field-effect-transistor(MOS FET), for its active element and the power drift of the amplifer. From these analytical considerations some design standardsn were found for the MOS FET differential amplifier available for the measurement of the very small current (pico-ampare range). A differential amplifier was designed and built in the view of above considerations. Its equivalent input gate voltages of the thermal drift and the power drift were 0.57mV/.deg. C in the range 25.deg. C-60.deg. C and 8.8mV/V in the range of 20% drift of its orginal value, respectively.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1060-1068
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• 2002

Compound continuously variable transmission(CVT) mechanisms are proposed, which can offer a backward mode, a geared neutral, an underdrive mode and an overdrive mode. They are composed of a 2K-H I type differential gear unit, a V-belt type continuously variable unit(CVU), a few friction clutches and gears, and not required of a starting device as a torque converter. Compound CVT mechanisms developed here present two distinct operating modes which are a power circulation mode and a power split mode. The transition of two modes takes place at the particular CVU speed ratio. For these CVT mechanisms, performance analysis related to speed ratio, power ratio and efficiency are executed and proven by experimental studies.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Journal of Mechanical Science and Technology
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• 제20권6호
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• pp.770-781
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• 2006

This paper defined design constraints for the compound CVTs (continuously variable trans-missions) by combining power-circulation-mode CVTs and power-split-mode CVTs, which were proposed for connecting 2K-H I-type differential gear to V-belt-type CVU (Continuously Variable Unit). The design constraints are the necessary and sufficient conditions to avoid geometrical interferences among elements in the compound CVTs, and to guarantee smooth assembly between the power-circulation-mode CVT and power-split-mode CVT Two com-pound CVTs were designed and manufactured in accordance with the design constraints. With these compound CVTs, theoretical analysis and performance experiments were conducted. The results showed that the design constraints were valid and effective design method, and that the designed compound CVTs had the improved performance.

• 대한수학회논문집
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• 제36권3호
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• pp.557-573
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• 2021

In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric ₂F₁(x) function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators. Formulas (images) for compositions of such generalized fractional integrals and differential constructions with the n-times product of the generalized modified Bessel function of the second type are established. The results are obtained in terms of the generalized Lauricella function or Srivastava-Daoust hypergeometric function. Equivalent assertions for the Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential are also deduced.