• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.833-845
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• 1997

Fourier expansion is considered for the deconvolution problem of estimating a probability density function when the sample observations are contaminated with random noise. In the log-Fourier method of density estimation for data without noise, the logarithm of the unknown density function is approximated by a trigonometric function, the unknown parameters of which are estimated by maximum likelihood. The log-Fourier density estimation method, which has been considered theoretically by Koo and Chung (1997), is studied for the finite-sample case with noise. Numerical examples using simulated data are given to show the performance of the log-Fourier deconvolution.

• Steel and Composite Structures
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• v.34 no.4
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• pp.615-623
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• 2020

In this paper, free vibration analysis of a functionally graded cylindrical nanoshell resting on Pasternak foundation is presented based on the nonlocal elasticity theory. A two-dimensional formulation along the axial and radial directions is presented based on the first-order shear deformation shell theory. Hamilton's principle is employed for derivation of the governing equations of motion. The solution to formulated boundary value problem is obtained based on a harmonic solution and trigonometric functions for various boundary conditions. The numerical results show influence of significant parameters such as small scale parameter, stiffness of Pasternak foundation, mode number, various boundary conditions, and selected dimensionless geometric parameters on natural frequencies of nanoshell.

• School Mathematics
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• v.1 no.2
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• pp.483-512
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• 1999

The purpose of the research was to investigate the patterns of student's mathematical thinking and behavior and describe the nature of difficulties the student underwent in trigonometry as the student conducted independent explorations within the interactive technology environment. Also, the research identified the connections among multiple representations and merits and shortcomings in using a graphic calculator as a tool. A take-based clinical interview procedure as the method for qualitative research was used to find the cognitive actions of the participant and his interactions with the graphic calculator. A case study report was written for the student. The researcher found that the student moved from operative stage, to constructive stage, to applicable stage of thinking. From Colgan; Graphing has significance both to mathematics and mathematics education in at least three ways since: * graphing represents an important technique, instrument and process in mathematics; * through ‘graphing’, per se, students can be said to be using one symbolic system to extend and acquire an understanding of another(e. g., trigonometric functions and their graphs). * graphing is propaedeutic to other, more advanced topics and concepts in mathematics.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.1
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• pp.31-37
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• 1985

An interesting area of application which makes use of the unique features of the walsh series is that on non-linear stochastic problems. In particular, some success has been obtained in improving the efficiency of signal detection for those transducers which are essentially non-linear in operation. The set of harmonically-related nonorthogonal triangle waves is shown to form a basis apanning the same function space representable by fourier(trigonometric) series. A method for generating nonorthogonal bases for signal representation is presented tailor-made basis function can be used for specific purposes. Fundamental proofs of the basis properties of the representation are examined along with examples illustrating the techniques and computer simulation.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1259-1277
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• 2015

In this work, a trigonometric refined beam theory for the bending, buckling and free vibration analysis of carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundation is developed. The significant feature of this model is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the Timoshenko beam (TBM) without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. To examine accuracy of the present theory, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending, buckling and free vibration responses of CNTRC beam are discussed.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.1
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• pp.42-50
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• 1987

The energy expressions are formulated for the axially stiffened shell treating the stiffeners as discrete elements. The principle of minimum potential energy is employed to formulate the buckling equations for a simply supported, axially stiffened shell under uniform axial compression. The displacement functions are expended into double trigonometric series. The mode assuming method employed in this paper makes it possible to reduce the matrix size of the eigenvalue problem considerably. Effects are made to investigate the transition from overall buckling to local buckling and to verify the existence of the minimum stiffness ratio of stiffener as in the case of stiffened plate. The results of the calculation show that the critical stiffener size increase linearly as the length of the shell increases. The results also show that the overall buckling load decreases and the local buckling load has a nearly constant value as the length of the shell increases. The results show very good agreements with other computational available.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.30 no.6
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• pp.929-935
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• 1997

The total energy of fish movement and the maximum burst swimming speed were estimated and formulated in accordance with body length and water temperature for several species in fisheries by empirical methods and also by using published results. Under the assumption of swimming energy reserve of a fish at the initial rest state, the swimming endurance of fish with different body lengths, swimming speeds and angular velocity was calculated using the relevant equations under similar conditions in tank experiments as well as natural conditions in field. Relative swimming energy efficiency or the transition swimming speed between red and white muscle for energy consumption was represented as a trigonometric function of swimming speed ratio. Therefore, this model does closely approach the actual swimming abilities and their limits especially in relation to the fishing gear operation and allow for the greater vitality of the wild fish in the fields.

• Proceedings of the Korea Database Society Conference
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• 1995.12a
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• pp.173-176
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• 1995

본 논문에서 다루는 내용은 멀티미디어 정보처리시 이용되는 여러 신호 처리용 하드웨어에서 필요로 하는 벡터 트랜스퍼메이션(Vector Transformation)및 오소그날 트랜스퍼메이션(Orthogonal Transformation)에 유용할 뿐만 아니라 여러 형태의 다양한 연산(elementary function including trigonometric functions)을 하나의 단일화된 알고리즘으로 구현할 수 있게 한 CORDIC(Coordinate Rotation Digit Computer)연산［1］［2］에 관한 연구이다. CORDIC 연산기를 실현함에 있어서 고속 연산을 위해 고속 가산기(fast adder)로서 CSA(Carry Save Adder)를 선택하는데, 본 논문의 연구 초점은 CORDIC연산기를 하드웨어로 실현하기 전에 Bit-Level의 시뮬레이터를 통하여, CSA의 특징상 발생할 수 있는 문제점어 대해 설명하고, 해결 방법［3］을 이용하여 원하는 값에 접근하는가를 확인하여 다양한 Bit의 조작으로 오차의 정도에 따라 유효한 CORDIC연산기를 실현하는데 도움이 되고자 한다.

• Proceedings of the KIPE Conference
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• 2005.07a
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• pp.578-580
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• 2005

This paper proposes the algorithm for the initial pole-position estimation of a surface PM-LSM, which is carried out under the pseudo-position control with-out a pole sensor and is insensitive to the motor parameters. This algorithm is based on the principle that the initial pole-position is calculated by the reverse trigonometric-function using the two reference currents, which are informed from the speed controller. The effectiveness of the proposed algorithm is confirmed by the arithmetical analysis and the experiment. IPP is well estimated within a satisfied moving-distance and a shorter estimation taken-time even if large disturbance such as cogging and friction are existed.