• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.65-74
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• 2015

In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.

• Proceedings of the KIEE Conference
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• 2003.07e
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• pp.55-57
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• 2003

This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. In this paper, the accuracy of the Block Pulse series coefficients derived by using the Lagrange second order interpolation polynomial is approved by the mathematical method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.310-323
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• 1990

A three-noded, with three degree-of-freedom at each node, in-plane curved beam element is formulated and employed in eigen-analysis of constant curvature beam. The conventional quadratic shape functions used in a three noded C .deg. type curved beam element produce such an undesirable large stiffness that a significant error is introduced in displacements and stresses. These phenomena are called 'Stiffness Locking Phenomena', which result from spurious strain energy due to inappropriate assumptions on independent isoparametric quadratic interpolation functions. Stiffness locking phenomena can be alleviated by using modified interpolation functions which get rid of spurious constraints of conventional interpolation functions. Eigenvalues and their modes as well as displacements and stresses may be locked because they are related to stiffness. Using modified curved beam element in eigenvalue problem of cantilever and arch, the property and performance of modified curved beam element are examined by numerical experimentations. In these eigen-analyses, mass matrices are calculated by using both modified and unmodified curved beam element, are compared with theoretical solutions. These comparisons show that the performance of the modified curved beam element is better than that of the unmodified curved beam element.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.279-284
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• 1994

Let R = ($r_1$, $r_2$, …, $r_{m}$) and S = ($s_1$, $s_2$, …, $s_{n}$ ) be positive integral vectors satisfying $r_1$＋ $r_2$＋…＋ $r_{m}$ = $s_1$＋ $s_2$＋ㆍㆍㆍ＋ $s_{n}$ , and let U(R, S) denote the class of all m $\times$ n matrices A = [$_a{ij}$ ] where $a_{ij}$ = 0 or 1 such that (equation omitted) = $r_{i}$ , (equation omitted) = $s_{j}$ , i = 1, ㆍㆍㆍ, m, j = 1, ㆍㆍㆍ, n.(omitted)

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.4
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• pp.89-95
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• 2007

There are various methods constructing correlation immune functions such as Siegenthaler's, Camion et al's and Seberry et al's. In particular, Soberry et al's is a method which directly constructs balanced correlation immune functions of any order using the theory of Hadamard matrices. In this paper, we have studied Seberry et al's method for constructing a correlation immune function on a higher dimensional space by combining known correlation immune functions on a lower dimensional space. Futhermore, we calculated the nonlinearity of functions which are constructed by combining of several correlation immune functions. That is, we have shown that the direct sum of two correlation immune functions and a combination of four correlation immune functions have higher nonlinearity in comparison with each functions. This functions in stream cipher are safe against correlation attacks.

• Structural Engineering and Mechanics
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• v.2 no.1
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• pp.95-112
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• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.151-167
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• 2006

A p-version of the finite element method in conjunction with the modeling dynamic method using the arc-length stretch deformation is considered to determine the bending natural frequencies of a cantilever flexible plate mounted on the periphery of a rotating hub. The plate Fourier p-element is used to set up the linear equations of motion. The transverse displacements are formulated in terms of cubic polynomials functions used generally in FEM plus a variable number of trigonometric shapes functions representing the internals DOF for the plate element. Trigonometric enriched stiffness, mass and centrifugal stiffness matrices are derived using symbolic computation. The convergence properties of the rotating plate Fourier p-element proposed and the results are in good agreement with the work of other investigators. From the results of the computation, the influences of rotating speed, aspect ratio, Poisson's ratio and the hub radius on the natural frequencies are investigated.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.9
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• pp.806-811
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• 2012

In this paper Hartley functions are used to approximate the solutions of continuous time linear dynamical system. The Hartley function and its integral operational matrix are first presented, an efficient algorithm to solve the Stein equation is proposed. The algorithm is based on the compound matrix and the inverse of sum of matrices. Using the structure of the Hartley's integral operational matrix, the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.791-806
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• 2004

The inverse pseudo excitation method is used in the identification of random loadings. For structures subjected to stationary random excitations, the power spectral density matrices of such loadings are identified experimentally. The identification is based on the measured acceleration responses and the structural frequency response functions. Numerical simulation is used in the optimal selection of sensor locations. The proposed method has been successfully applied to the loading identification experiments of three structural models, two uniform steel cantilever beams and a four-story plastic glass frame, subjected to uncorrelated or partially correlated random excitations. The identified loadings agree quite well with actual excitations. It is proved that the proposed method is quite accurate and efficient in addition to its ability to alleviate the ill conditioning of the structural frequency response functions.

• Structural Engineering and Mechanics
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• v.7 no.3
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• pp.259-276
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• 1999

An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.