• The KIPS Transactions:PartA
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• v.11A no.7 s.91
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• pp.571-576
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• 2004

In this paper, by using Lagrange polynomial interpolation with a trick such that for $f(x)^{3}$ we shall use $f(x_i)^{3}I_i(x)^{3}$ instead of $I(x)^{3}$ where $I{x}{\;}={\;}\sum_{i}^{f}(x_i)I_i(x)$. We show the convergence and stability and calculate errors. These errors are approximately less than $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ where N is a polynomial degree.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.3-10
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• 1978

Let $X_i,...,X_n$ be a random sample from a distribution with cumulants $K_1, K_2,...$. The statistic $t = \frac{\sqrt{x}(\bar{X}-K_1)}{S}$ has the well-known 'student' distribution with $\nu = n-1$ degrees of freedom if the $X_i$ are normally distributed (i.e., $K_i = 0$ for $i \geq 3$). An Edgeworth series expansion for the distribution of t when the $X_i$ are not normally distributed is obtained. The form of this expansion is Prob $(t

• Proceedings of the IEEK Conference
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• 2002.06d
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• pp.299-302
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• 2002

Digital video camera can be a useful tool to capture images for use in colorimeter. However, the RGB signals generated by different digital video camera are not equal for the same scene. The digital video camera for use in colorimeter is characterized based on the CIE standard colorimetric observer. One method of deriving a colorimetric characterization matrix between camera RGB output signals and CIE XYZ tristimulus values is Polynomial modeling. In this paper, 3${\times}$3 linear matrix and 3${\times}$l1 polynomial matrix is used to investigate the characterization performance of the professional digital video camera. In experimental results, it is demonstrated that proposed 3${\times}$3 linear matrix has a reasonable degree of accuracy for use in colorimeter.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.51-59
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• 1996

A measure that quantifies the amount of slope retatability for the second degree Scheffe polynomial model for mixture experiments is proposed and used to compare the several mixture designs which met the symmetric momemts conditions in this article.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.323-329
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• 2022

Let $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ be a polynomial of degree n and $p^{\prime}(z)$ its derivative. If $\max\limits_{{\mid}z{\mid}=r}{\mid}p(z){\mid}$ is denoted by M(p, r). If p(z) has all its zeros on |z| = k, k ≤ 1, then it was shown by Govil [3] that $$M(p^{\prime},\;1){\leq}\frac{n}{k^n+k^{n-1}}M(p,\;1)$$. In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.425-431
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• 2022

Let ℤ and ℚ be the ring of integers and the field of rational numbers, respectively. Let h(ℤ, ℚ) be the ring of composite Hurwitz polynomials. In this paper, we study the factorization of composite Hurwitz polynomials in h(ℤ, ℚ). We show that every nonzero nonunit element of h(ℤ, ℚ) is a finite *-product of quasi-primary elements and irreducible elements of h(ℤ, ℚ). By using a relation between usual polynomials in ℚ[x] and composite Hurwitz polynomials in h(ℤ, ℚ), we also give a necessary and sufficient condition for composite Hurwitz polynomials of degree ≤ 3 in h(ℤ, ℚ) to be irreducible.

• Korean Journal of Veterinary Research
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• v.26 no.1
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• pp.175-185
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• 1986

The measurement of angled erythrocyte sedimentation rate (ESR), as a replacement for perpendicular ESR, for cattle blood was scrutinized since it has been well known that perpendicular ESR in cattle is too slow to be adopted as an effective clinical test. Samples of blood were taken from 186 Korean native cattle over 2 years old. The results obtained in the experiment were summarized as follows. 1. Average values of perpendicular ESR/24hrs in 15 apparently healthy cattle, as measured by Wintrobe, Westergren and capillary tubes, were $5.8{\pm}2.2$, $11.1{\pm}3.7$ and $10.4{\pm}4.5%$ respectively, which were found to be similar to the values of perpendicular ESR/hr of normal blood of human. 2. The ESR was determined in the tubes held at 90, 75, 60, 45, 30 and 15-degree angles, using 3 types of tubes. For the diagnostic purposes, the best results were obtained from the tubes held at 45-degree angle. 3. The angled ESR values increased as the diameters of the tube-bores decreased. 4. The tube length did not affect the angled ESR(%). 5. The angled ESR values increased with the increased environmental temperature during the ESR measurement. 6. The storage temperature at $5^{\circ}C$, $20^{\circ}C$ and $35^{\circ}C$, of the blood for 24 hours did not affect the angled ESR. 7. Samples of blood were treated with 4 kinds of anticoagulants (heparin, $K_2$-EDTA, double oxalate and sodium citrate) and the ESR was determined at 45-degree angle, using capillary hematocrit tubes. The ESR values were higher in the blood samples treated with sodium citrate than in those treated with other anticoagulants. 8. By using the autologous plasma, the PCV was adjusted to be 5, 10, 20, 30, 40 and 50ml/100ml and the ESR was determined in the capillary hematocrit and Wintrobe tubes held at 45 degrees. In both of the methods the ESRs increased as the values of PCV decreased. The regressions of ESR to PCV in both 45-degree-angled capillary and Wintrobe tubes were curvilinear. For the capillary hematocrit tubes the second degree polynomial $Y=61.9779-2.3533x+0.0228x^2$ (r=0.9999) fits the data. And in the case of Wintrobe tubes the second degree polynomial $Y=27.9767-1.1314x-0.0117x^2$ (r=0.9998) fits the data. 9. The 45-degree angled ESR was determined in the blood of 71 healthy Korean native cows using capillary hematocrit tubes. The average PCV was $35.4{\pm}3.6ml/100ml$. The observed ESR/hr averaged $7.2{\pm}2.7%$, while the corrected ESR/hr to a PCV of 36ml/100ml averaged $6.6{\pm}1.3%$. From these results it was concluded that to obtain the best results the ESR/hr of Korean native cattle should be determined at 45-degree angle at room temperature($20^{\circ}C$) using capillary hematocrit tubes.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.3
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• pp.628-636
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• 2010

In this paper, we present a new type high speed parallel multiplier for performing the multiplication of two polynomials using standard basis in the finite fields GF($2^m$). Prior to construct the multiplier circuits, we design the basic cell of vector code generator(VCG) to perform the parallel multiplication of a multiplicand polynomial with a irreducible polynomial and design the partial product result cell(PPC) to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial with VCG circuits. The presented multiplier performs high speed parallel multiplication to connect PPC with VCG. The basic cell of VCG and PPC consists of one AND gate and one XOR gate respectively. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields GF($2^4$). Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper uses the VCGs and PPCS repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSL.

• Journal of Information Processing Systems
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• v.10 no.3
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• pp.395-411
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• 2014

Temporal medical data is often collected during patient treatments that require personal analysis. Each observation recorded in the temporal medical data is associated with measurements and time treatments. A major problem in the analysis of temporal medical data are the missing values that are caused, for example, by patients dropping out of a study before completion. Therefore, the imputation of missing data is an important step during pre-processing and can provide useful information before the data is mined. For each patient and each variable, this imputation replaces the missing data with a value drawn from an estimated distribution of that variable. In this paper, we propose a new method, called Newton's finite divided difference polynomial interpolation with condition order degree, for dealing with missing values in temporal medical data related to obesity. We compared the new imputation method with three existing subspace estimation techniques, including the k-nearest neighbor, local least squares, and natural cubic spline approaches. The performance of each approach was then evaluated by using the normalized root mean square error and the statistically significant test results. The experimental results have demonstrated that the proposed method provides the best fit with the smallest error and is more accurate than the other methods.

• The Journal of Natural Sciences
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• v.4
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• pp.191-220
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• 1991

A new texture segmentation-based image coding technique which performs segmentation based on roughness of textural regions and properties of the human visual system (HVS) is presented. This method solves the problems of a segmentation-based image coding technique with constant segments by proposing a methodology for segmenting an image texturally homogeneous regions with respect to the degree of roughness as perceived by the HVS. The fractal dimension is used to measure the roughness of the textural regions. The segmentation is accomplished by thresholding the fractal dimension so that textural regions are classified into three texture classes; perceived constant intensity, smooth texture, and rough texture. An image coding system with high compression and good image quality is achieved by developing an efficient coding technique for each segment boundary and each texture class. For the boundaries, a binary image representing all the boundaries is created. For regions belonging to perceived constant intensity, only the mean intensity values need to be transmitted. The smooth and rough texture regions are modeled first using polynomial functions, so only the coefficients characterizing the polynomial functions need to be transmitted. The bounda-ries, the means and the polynomial functions are then each encoded using an errorless coding scheme. Good quality reconstructed images are obtained with about 0.08 to 0.3 bit per pixel for three different types of imagery ; a head and shoulder image with little texture variation, a complex image with many edges, and a natural outdoor image with highly textured areas.