• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.12
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• pp.1273-1279
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• 1991

In this paper new adaptive approach method for sub optimal control of nonlinear systems is presented. This paper used the method proposed by J.P.Matuszewski for adaptive optimal control scheme and used block pulse transformations for solving the Riccati differential equation which is usually quite this method is estabilished with simulation results and comparisons to existing approaches.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.705-714
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• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05b
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• pp.160-165
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• 1998

Under the heavy irradiation, when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriated transformation of these nonlinear differential equations to soluble Poisson's equations, so that analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.151-156
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• 1999

Under the heavy irradiation of crystalline materials when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriate transformation of these nonlinear differential equations to more solvable Poisson's equations, finally analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Structural Engineering and Mechanics
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• v.12 no.6
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• pp.657-668
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• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.7 no.3
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• pp.428-436
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• 1997

Hexacelsian ($BaO{\cdot}Al_2O_3{\cdot}2SiO_2$) powder was prepared by a solution-polymerization route employing PVA solution as a polymeric carrier. A fine amorphous-type hexacelsian powder with an average particle size of 0.8 $\mu \textrm{m}$ and a BET specific surface area of $63 \textrm{m}^2$/g was made by a ball-milling the powder precursor for 12 h after calcination at $800^{\circ}C$ for :1 h. A densified hexacelsian was obtained through sintering at $1550^{\circ}C$ for 2 h under an air atmosphere. The $\alpha\longleftrightarrow\beta$ and $\beta\longleftrightarrow\gamma$ displacive phase transformation in polycrystalline hexacelsia,n was examined by using dilatometry and differential scanning calorimtry. The reconstructive transformation between hexacelsian and celsian was obtained by annealing at $1600^{\circ}C$ for 72h. Volume contraction of 5.6% was accompanied by the reconstructive transformation.

• Korean Journal of Materials Research
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• v.10 no.6
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• pp.392-397
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• 2000

The effect of pressure on the phase transformation in Fe-30Ni-0.35C Alloy and pure metals was investigated by using PDSC(pressure differential scanning calorimeter). As the pressure increased from 1 atm to 60 atm, the $A_s$points of the ausformed martensite and the marformed martensite in Fe-30Ni-0.35C Alloy were lowered about $2~4^{\circ}C$ at reverse transformation. This is why the volume change came down at phase transition(from martensite to autenite). As the pressure increased from 1 atm to 60 atm, $A_f$ points were constant or slightly increased. This is due to the promotion of carbide precipitation with increasing pressure. The enthalpy change of the ausformed martensite in Fe-30Ni-0.35C Alloy was increased by 10~14J/g. The melting points of the pure metals, Se, Sn, Pb, Zn and Te were slightly increased with increasing pressure. The enthalpy changes of the pure metals at melting were little changed or slightly increased with increasing pressure.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1462-1470
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• 2003

According to the necessity about information security as well as the advance of IT system and the spread of the Internet, a variety of cryptography algorithms are being developed and put to practical use. In addition the technique about cryptography attack also is advanced, and the algorithms which are strong against its attack are being studied. If the linear transformation matrix in the block cipher algorithm such as Substitution Permutation Networks(SPN) produces the Maximum Distance Separable(MDS) code, it has strong characteristics against the differential attack and linear attack. In this paper, we propose a new algorithm which cm estimate that the linear transformation matrix produces the MDS code. The elements of input code of linear transformation matrix over GF$({2_n})$ can be interpreted as variables. One of variables is transformed as an algebraic formula with the other variables, with applying the formula to the matrix the variables are eliminated one by one. If the number of variables is 1 and the all of coefficient of variable is non zero, then the linear transformation matrix produces the MDS code. The proposed algorithm reduces the calculation time greatly by diminishing the number of multiply and reciprocal operation compared with the conventional algorithm which is designed to know whether the every square submatrix is nonsingular.

• Smart Structures and Systems
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• v.9 no.3
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• pp.231-251
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• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• Journal of the Korean Society for Heat Treatment
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• v.22 no.1
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• pp.3-7
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• 2009

Variation in oxidation behavior with heat treatment temperature is investigated for a Ni-Ti alloy using X-ray diffraction, DSC (differential scanning calorimetry) and Auger electron spectroscopy. And the effect of oxidation on transformation behavior and superelasticity is characterized. A cold-worked 50.6Ni-Ti alloy is oxidized at 300-$700^{\circ}C$ for 1 hr in the air atmosphere. With an increase in heating temperature, the structure of $TiO_2$ changes from amorphous (300 and $400^{\circ}C$) to anatase ($500^{\circ}C$), and to rutile ($700^{\circ}C$). Activation energy of oxidation for NiTi is measured to be 51 Kcal/mol when heating temperature is $500^{\circ}C$ or above. Since Ti reacts preferably with oxygen, Ni content increases between matrix and oxide, forming $Ni_{3}Ti$ compounds. The resultant of oxidation decreases significantly $M_s$ and $A_s$ temperature in the specimen oxidized at $900^{\circ}C$ with $B_2{\rightarrow}M$ transformation path. An extra is found on cooling between two peaks in the specimen with $B_2{\rightarrow}R{\rightarrow}M$ one which is oxidized at $900^{\circ}C$ and aged at $500^{\circ}C$. Oxidation deteriorates superelasticity due to formation of Ni-rich compound.