• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.22-32
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• 2002

V-notched crack problems can be formulated as eigenvalue problems. The problem ova v-notched crack in anisotropic and/or pseudo-isotropic dissimilar materials was formulated as an eigenvalue problem to discuss stress singularities. The eigenvalue problem was served by the commercial numerical program; MATHEMATICA. The specific data of eigenvalues possessing the stress singularity were obtained. Stress singularities fur v-notched cracks in anisotropic and/or pseudo-isotropic dissimilar materials were discussed according to the relation between wedge angle and material property. It was shown that there are three cases of eigenvalues possessing the stress singularity; one real, two real and one complex.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2002.11a
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• pp.149-152
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• 2002

본 논문에서는 하드웨어의 Serail Number를 사용하여 보다 대중성 있고, 이동성이 있는 인증방법에 대하여 제안하였다. 서론에서는 컴퓨터 내부와 외부에 연결되는 Device ID들과 관련하여 각각의 선택에 대한 장단점을 알아보았고, 다음으로 이동성을 향상시키기 위해 대중화된 Device를 사용하는 것에 대해 말하였고, 대중화된 Device들을 사용하여 어떻게 적용을 시키는지에 대해 알아보았다. 마지막으로 본 논문이후로 연구되어야하는 부분에 대해 알아보았다. Wolfram Research에서 만들어진 Mathematica라는 프로그램에서 사용되는 Machine ID에 대하여 먼저 알아보았고, Machine ID를 사용하여 일반 유지들이 사용하고 있는 인터넷 뱅킹 등에 사용되는 인증서를 보다 안전하고 이동성 있게 사용할 수 있는 방안으로 클라이언트에서 서버로 인증서가 확인이 된 후, 서버에서 다시 클라이언트로 갱신된 인증서를 보내어, 사용자는 갱신된 인증서에서만 다음 번 접속이 가능하도록 하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.201-202
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• 2008

Because of the importance of suction or injection in the fields of aerodynamics, space science and many other industrial applications, our present study is motivated. The effect of natural convection on MHD flow past a vertical plate with suction or injection is studied. We have tried to solve the dimensionless governing equations by using finite difference scheme. To ensure the validity of our numerical solutions, we have compared our numerical solutions for temperature and velocity for the case of suction and injection for unit Prandtl number with the available exact solutions in the literature. The corresponding codes were written in Mathematica 5.0 for calculating numerical solutions for temperature and velocity and the comparison between the exact and numerical solutions. For the purpose of discussing the results some numerical calculations are carried out for non-dimensional temperature T, velocity u, skin friction ${\tau}$ and the Nusselt number $N_u$, by making use of it, the rate of heat transfer is studied.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.4 no.3
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• pp.39-47
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• 1995

This paper suggests generalize mathematica mode for the benefit of volumetric error analysis of a multi-axis machine tool machining a sculptured surfaces. The volumetric error, in this paper, is defined as a three dimensional error at the cutting point, which is caused by the geometric errors and the kinematic errors of each axis and alignment errors of the cutting tool. The actual cutting position is analyzed based on the form shaping model including a geometric error of the moving carriage, where a form shaping model is derived from the homogeneous transformation matrix. Then the volumetric error is obtained by calculating the position difference between the actual cutting position and the ideal one calculated from a Nonuniform Rational B-Spline named as NURES. The simulation study shows the effectiveness for predicting the behavior of machining error and for the method of error compensation.

• The Mathematical Education
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• v.41 no.2
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• pp.203-213
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• 2002

In this paper, we introduce the concepts of geometric and arithmetic triangles. Geometric and arithmetic triangles are special types of rational Heron triangles - triangles with rational sides and area. In addition, the theory illustrated in this paper gives certain theorems on the determination of non-right angled geometric and arithmetic triangles. In the meantime, with the help of Mathematica, we compute the sides and area of several triangles(GRT, IGT, RIGT, RAT). Since the material presented in this paper is within the reach of undergraduates, it can attract attention of mathematics students and may also be of interest to the mathematicians. In this content we believe this paper can help undergraduates to have interests in the new world of mathematics.

• Research in Mathematical Education
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• v.11 no.2
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• Structural Engineering and Mechanics
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• v.47 no.3
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• pp.345-359
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• 2013

For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius' scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.221-238
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• 2008

Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load, buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

• Journal of Astronomy and Space Sciences
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• v.32 no.2
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• pp.151-159
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• 2015

The fundamental conception in physics of the propagation of the electromagnetic wave polarization in matter is newly understood as the cardinal keyword in free-space quantum communication technology and cosmology in astrophysics. Interactive visualization of the propagation mechanism of polarized electromagnetism in a medium with its helicity has accordingly received attention from scientists exploiting the protocol of quantum key distribution (QKD) to guarantee unconditional security in cryptography communication. We have provided a dynamic polarization platform for presenting the polarization modes of a transverse electromagnetic wave, converting the state of polarization through the arrangement of optical elements, using Jones vectors calculations in Methematica. The platform graphically simulates the mechanism of production and propagation of the polarized waves in a medium while satisfying Maxwell's equations.

• Coupled systems mechanics
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• v.5 no.1
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• pp.59-86
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• 2016

This paper deals with the free vibration analysis of a dynamical coupled system: flexible gravity dam- compressible rectangular reservoir. The finite element method is used to compute the natural frequencies and modal shapes of the system. Firstly, the reservoir and subsequently the dam is modeled by classical 8-node elements and the natural frequencies plus modal shapes are calculated. Afterwards, a new 21-node element is introduced and the same procedure is conducted in which an efficient method is employed to carry out the integration operations. Finally, the coupled dam-reservoir system is modeled by solely one 21-node element and the free vibration of dam-reservoir interaction system is investigated. As an important result, it is clearly concluded that the one high-order element treats more precisely than the eight-node elements, since the first one utilizes fifth-degree polynomials to construct the shape functions and the second implements polynomials of degree two.