• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.269-283
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• 2013

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.649-652
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• 2007

In this note we provide a generalization of the Schur-Cohn test. If $p_n$ be a polynomial of degree n then $p_n$ is a reduced-stable polynomial whose reduced degree is equal to r if and only if $D_n\;:=\;P_nQ_n^{-1}$ is a contraction such that rank ($I-D_nD_n^*$) = r.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.179-192
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• 1997

An algorithm to get an optimal choice for the number of symmetric quadrature points is given to find symmetric quadrature points is given to find symmetric quadrature for-mulas over a unit disk with a minimal number of points even when a high degree of polynomial precision is required. The symmetric quad-rature formulas for numerical integration over a unit disk of complete polynomial functions up to degree 19 are presented.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.183-202
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• 2018

${\Delta}-moves$ are closely related with a Vassiliev invariant of degree 2. For classical knots, M. Okada showed that the second coefficients of the Conway polynomials of two knots differ by 1 if the two knots are related by a single ${\Delta}-move$. The first author extended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knots of type 2 which is induced from the Kauffman polynomial of a virtual knot. The arrow polynomial is a generalization of the Kauffman polynomial. We will generalize this result by using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knot and give a lower bound for the number of ${\Delta}-moves$ transforming $K_1$ to $K_2$ if two virtual knots $K_1$ and $K_2$ are related by a finite sequence of ${\Delta}-moves$.

• Nuclear Engineering and Technology
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• v.31 no.3
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• pp.303-313
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• 1999

Various interpolation methods have been compared for reconstruction of LMR pin power distributions in hexagonal geometry. Interpolation functions are derived for several combinations of nodal quantities and various sets of basis functions, and tested against fine mesh calculations. The test results indicate that the interpolation functions based on the sixth degree polynomial are quite accurate, yielding maximum interpolation errors in power densities less than 0.5%, and maximum reconstruction errors less than 2% for driver assemblies and less than 4% for blanket assemblies. The main contribution to the total reconstruction error is made tv the nodal solution errors and the comer point flux errors. For the polynomial interpolations, the basis monomial set needs to be selected such that the highest powers of x and y are as close as possible. It is also found that polynomials higher than the seventh degree are not adequate because of the oscillatory behavior.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1491-1501
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• 2018

Polynomials with all the coefficients in {0, 1} and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in {-1, 1} are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine the set of Littlewood polynomials of degree at most 12 which divide Newman polynomials. Moreover, we show that every Newman quadrinomial $X^a+X^b+X^c+1$, 15 > a > b > c > 0, has a Littlewood multiple of smallest possible degree which can be as large as 32765.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.659-675
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• 2023

Let K be an algebraically closed field of characteristic 0 and let f be a non-fibered planar quadratic polynomial map of topological degree 2 defined over K. We assume further that the meromorphic extension of f on the projective plane has the unique indeterminacy point. We define the critical pod of f where f sends a critical point to another critical point. By observing the behavior of f at the critical pod, we can determine a good conjugate of f which shows its statue in GIT sense.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.57-66
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• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.

• Journal of Power System Engineering
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• v.3 no.4
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• pp.69-78
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• 1999

In the single-input and single-output system, the parameter of plant is scalar polynomial, but in the multiple input and multiple output, it accompanies, being matrix polynomial, the consideration of observable controlability index or problems non-commutation in matrix polynomial as well as degree, and it is more complex to deal with. Therefore, it is thought that a full research on the single-input and single-output system is not sufficient. This paper proposes that problems of minimum variance self-tuning regulator by using numerical calculation example of multivariable system and pole assignment self-tuning regulator.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.427-438
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• 2005

From a notion of d-pseudo-orthogonality for a sequence of poly-nomials ($d\;\in\;{2,3,\cdots}$), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972, 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.