• Journal of applied mathematics & informatics
• /
• 제5권3호
• /
• pp.735-748
• /
• 1998

We analyze the error in the p version of the of the finite element method when the effect of the quadrature error is taken in the load vector. We briefly study some results on the $H^{1}$ norm error and present some new results for the error in the $L^{2}$ norm. We inves-tigate the quadrature error due to the numerical integration of the right hand side We present theoretical and computational examples showing the sharpness of our results.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.65-79
• /
• 2007

An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.

• Current Optics and Photonics
• /
• 제3권3호
• /
• pp.204-209
• /
• 2019

In an optical interferometer that uses sinusoidal modulation and quadrature detection, the amplitude and offset of the interference signal vary with time, even without considering system noise. As a result, the circular Lissajous figure becomes elliptical, with wide lines. We propose and experimentally demonstrate a method for compensating quadrature detection error, based on digital signal processing to deal with scaling and fitting. In scaling, fluctuations in the amplitudes of in-phase and quadrature signals are compensated, and the scaled signals are fitted to a Lissajous unit circle. To do so, we scale the average fluctuation, remove the offset, and fit the ellipse to a unit circle. Our measurements of a target moving with uniform velocity show that we reduce quadrature detection error from 5 to 2 nanometers.

• 대한수학회논문집
• /
• 제16권4호
• /
• pp.691-701
• /
• 2001

We computed zero mean Gaussian of average error bounds pf Simpsons quadrature with convariances in [2]. In this paper, we compute zero mean Gaussian of average error bounds between Simpsons quadrature and composite Simpsons quadra-ture on four consecutive subintervals. The reason why we compute these on subintervals is because these results enable us to compute a posteriori error bounds on the whole interval in the later paper.

• Korean Journal of Mathematics
• /
• 제8권1호
• /
• pp.47-52
• /
• 2000

We describe some results for the $h$ version which pertain to the questions on numerical quadrature. We also present an example that illustrates the rate of convergence predicted for linear elements under certain quadrature schemes in [2], [4], [5].

• ETRI Journal
• /
• 제28권6호
• /
• pp.793-795
• /
• 2006

When quadrature error exists, the shape of the M-ary phase shift keying (MPSK) signal constellation becomes skewed-elliptic. Each MPSK symbol takes on a different symbol error probability (SEP) value. The analytical results presented thus far have been derived from studies which examined the SEP problem assuming that the SEP of each MPSK symbol is equally likely; therefore, those results should not be treated as offering a complete solution. In this letter, we present a new and more complete solution to the SEP problem of MPSK by relaxing the above assumption and finding the expressions for the average as well as individual SEP in the presence of quadrature error.

• Korean Journal of Mathematics
• /
• 제10권2호
• /
• pp.179-190
• /
• 2002

We analyze the error in the $p$ version of the of the finite element method when the effect of the quadrature error is taken into account. We investigate source of quadrature error due to the presence of mapped elements. We present theoretical and computational examples regarding the sharpness of our results.

• 대한수학회지
• /
• 제34권4호
• /
• pp.911-925
• /
• 1997

We derive quadrature formulas for approximating wavelet coefficients for smooth functions from equally spaced point values with arbitrarily high degree of accuracy. Wa also estimate the error of quadrature formulas.

• 반도체디스플레이기술학회지
• /
• 제21권4호
• /
• pp.132-137
• /
• 2022

In this paper, we have studied the quadrature error reduction for the single drive 3-axis MEMS Gyroscope. There was a limitation of the previous study which is the z-axis quadrature error was large. To reduce this value, design methodologies were presented. And the methodologies included a different mesh application, z-rate spring structure change, and mass compensation for balancing of the structure. We conducted the modal analysis, drive mode analysis and sense mode analysis using COMSOL Multiphysics. As a result, a drive resonant frequency was 26003 Hz, with the x-sense, y-sense, z-sense being 26749 Hz, 26858 Hz, 26920 Hz, respectively. And the Mechanical sensitivity was computed at 2000 degrees per second(dps) input angular rate while the sensitivity for roll, pitch, and yaw was computed 0.011, 0.012, and 0.011 nm/dps respectively. And z-axis quadrature error was successfully improved, 2.78 nm to 0.95 nm, which the improvement rate was about 66 %.

• Journal of Communications and Networks
• /
• 제10권3호
• /
• pp.253-257
• /
• 2008

In this paper, the performance of generic orthogonal space-time block codes (OSTBCs) introduced by Alamouti [2], Tarokh [3], and Su and Xia [11] is analyzed. We first define one-dimensional component symbol error function (ODSEF) from the exact expression of the pairwise error probability of an OSTBC. Utilizing the ODSEF and the bit error probability (BEP) expression for quadrature amplitude modulation (QAM) introduced by Cho and Yoon [9], the exact closed-form expressions for the BEP of linear OSTBCs with QAM in quasi-static Rayleigh fading channel are derived. We also derive the exact closed-form of the BEP for some OSTBCs which have at least one message symbol transmitted with unequal power via all transmit antennas.