• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1445-1457
• /
• 2016

For a positive integer N divisible by 4, let ${\mathcal{O}}^1_N({\mathbb{Q}})$ be the ring of weakly holomorphic modular functions for the congruence subgroup ${\Gamma}^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring ${\mathcal{O}}^1_N({\mathbb{Q}})$ over ${\mathbb{Q}}$ in terms of both Fricke functions and Siegel functions, from which we are able to classify all Fricke families of such level N.

• Journal of the Korean Mathematical Society
• /
• v.61 no.5
• /
• pp.997-1033
• /
• 2024

We use Borcherds products to give a new construction of the weight 3 paramodular nonlift eigenform f_N for levels N = 61, 73, 79. We classify the congruences of f_N to Gritsenko lifts. We provide techniques that compute eigenvalues to support future modularity applications. Our method does not compute Hecke eigenvalues from Fourier coefficients but instead uses elliptic modular forms, specifically the restrictions of Gritsenko lifts and their images under the slash operator to modular curves.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
• /
• v.3 no.2
• /
• pp.16-21
• /
• 1992

The TE-mode characteristics of scattering and reception by a flanged parallel-plate waveguide are examined. The technique of the Fourier transform is used to represent the scattered fields in the spectral domain. The simultaneous equations for the transmitted field coefficients are solved to obtain the solution in an asymptotic series form. The numerical computations are performed to illustrate the behaviors of the scattered field and the transmission coefficients versus the aperture size.

• The Transactions of the Korean Institute of Electrical Engineers C
• /
• v.53 no.10
• /
• pp.539-545
• /
• 2004

In this paper, we consider the problem of capacitance matrix calculation for strip-line and other interconnects crossings. The problem is formulated in the spectral domain using the method of moments. Sinc-functions are employed as basis functions. Conventionally, such a formulation leads to a large, non-sparse system of linear equations in which the calculation of each of the coefficient requires the evaluation of a Fourier-Bessel integral. Such calculations are computationally very intensive. In the method proposed here, we provide simplified expressions for the coefficients in the moment method matrix. Using these simplified expressions, the coefficients can be calculated very efficiently. This leads to a fast evaluation of the capacitance matrix of the structure. Computer simulations are provided illustrating the validity of the method proposed.

• Tribology and Lubricants
• /
• v.19 no.6
• /
• pp.349-356
• /
• 2003

A damper floating ring seal with round hole pattern surfaces is suggested for better leakage control. The flat plate test of the round hole pattern surfaces has been performed to yield an empirical friction factor model. The exact predictions of the lock­up position of the damper floating ring, the leakage performance, and the rotordynamic coefficients of the seal are necessary to evaluate the rotordynamic performance of the turbo pump unit. The governing equations including the empirical friction factor model for round hole pattern surfaces are solved by the Fast Fourier Transform method. The lock­up position, leakage flow rate, and rotordynamic coefficients are evaluated according to the geometric parameters of the damper floating ring seal. Theoretical results show that the damper floating ring seals yield less leakage and better rotordynamic stability than the floating ring seal with a smooth surface.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.26 no.11
• /
• pp.1880-1885
• /
• 1989

In this paper, a new approach for systolic array realizing the discrete cosine transform (DCT) based on discrete Fourier transform (DFT) of an input sequence is presented. The proposed array is based on a simple modified DFT(MDFT) version of the Goertzel algorithm combined with Kung's approach and is proved perfectly. This array requires N cells, one multiplier and takes N clock cycles to produce a complete N-point DCT and also is able to process a continuous stream of data sequences. We have analyzed the output signal-to-noise ratio(SNR) and designed the circuit level layout of one-PE chip. The array coefficients are static adn thus stored-product ROM's can be used in place of multipliers to limit cost as eliminate errors due to coefficients quantization.

• Fibers and Polymers
• /
• v.1 no.1
• /
• pp.59-65
• /
• 2000

In order to investigate psychoacoustic characteristics of fibers, and to compare them with sound physical parameters, each sound of 25 different fabrics consisted of a single fiber such as wool, cotton, silk, polyester, and nylon was recorded. Sounds of specimens were transformed into critical band diagram and psychoacoustic characteristics including loudness and sharpness for each sound were calculated based on Zwicker＇s models. Physical parameters such as the level pressure of total sound (LPT), level ranges (ΔL), frequency differences (Δf), AR coefficients (ARC, ARF, ARE) were obtained in fast fourier transform (FFT) spectrum. Nylon taffeta showed higher values for loudness than 2.5 sone corresponding to human low conversation, while most silk fibers generated less louder showing lower values for loudness than 1.0 sone. Wool fibers had higher loudness mean value than that of cotton, while the two fibers didn't differ in LPT. Loudness showed high positive correlation coefficients with both LPT and ARC. Sharpness values were higher for wool fiber group than other fibers. Sharpness was not concerned with loudness, LPT, and ARC, but the fabrics with higher values for sharpness tended to show higher ΔL.

• The KSFM Journal of Fluid Machinery
• /
• v.4 no.3 s.12
• /
• pp.29-38
• /
• 2001

The floating ring seal has the ability of minimizing clearance without the rubbing phenomenon. It is often used in the turbo pump units of liquid rocket engines due to its superior leakage performance. The exact prediction of the lock-up position of the floating ring, the leakage performance, and the rotordynamic coefficients of the seal is necessary to evaluate the rotordynamic performance of the turbo pump unit. The governing equations(which are based on the Bulk-flow Model) we solved by the Fast Fourier Transform method. The lock-up position, leakage flow rate, and rotordynamic coefficients are evaluated according to the geometric parameters of the floating ring seal.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.05a
• /
• pp.528-534
• /
• 2001

Basic equations and its solution procedure are derived for the analysis of an annular pump seal in which the rotor has a large static displacement from the centered position. The Bulk-flow is assumed for a control volume set in the seal clearance and the flow is assumed to be completely turbulent in axial and circumferential direction. Moody's wall-friction-factor formula is used for the calculation of wall shear stresses in the control volume. For the reaction force developed by the seal, linearized zeroth-order and first-order perturbation equations are developed for small motion about an eccentric position. Flow variables are expanded by using Fourier series for the solution procedure. Integration of the resultant first-order pressure distribution along and around the seal defines the 12 elements of rotordynamic coefficients of the eccentric annular pump seal. The results of leakage and rotordynamic coefficients are presented and compared with the Marquette's experimental results and the San Andres' theoretical analysis.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.31-48
• /
• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.