• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.83-86
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• 2007

We determine the largest integer i such that $0 and the coefficient of $t^{i}$ is odd in the polynomial $(1+t+t^{2}+{\cdots}+t^{n})^{n+1}$. We apply this to prove that the co-index of the tangent bundle over $FP^{n}$ is stable if $2^{r}{\leq}n<2^{r}+\frac{1}{3}(2^{r}-2)$ for some integer r.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10a
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• pp.539-543
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• 1990

In this paper, we present a method of parameterizing LQG which simultaneously stabilizes a set of plant model by employing the well known separation principle and Hurwith polynomial. A conditions for existence of simultaneously stabilizing LQG for, given set of plant is drived. We show that suggested parameterization achieves the closed loop stability by fixed LQG for given set of plant.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.2
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• pp.215-220
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• 2004

In this paper, some algorithms for robust stabilization of linerar time - invariant single - input - multi output (SIMO) systems subject to parameter perturbatations are presented. At first, the determination algorithm of the largest stable hypersphere in the parameter space of a given characteristic polynomial with its coefficient perturbations near some stable nominal values is presented. These algorithms iteratively enlarge the stability hypersph ere in plant parameter space and can be used to design a controller to stabilize a plant subject to givien range of parameter ecxursions.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.93-100
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• 1998

The researches of Linear Programming are Khachiyan Method, which uses Ellipsoid Method, and Karmarkar, Affine, Path-Following and Interior Point Method which have Polynomial-Time complexity. In this study, Karmarkar Method is more quickly solved as 50 times then Simplex Method for optimal solution. but some special problem is not solved by Karmarkar Method. As a result, the algorithm by APL Language is proved time efficiency and optimal solution in the Primal-Dual interior point algorithm. Furthermore Karmarkar Method and Primal-Dual interior point Method is compared in some examples.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.34 no.12
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• pp.472-484
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• 1985

A design of robust voltage controller for high speed excitation of synchronous machine was carried out by pole assignment techniques. An affine map from characteristic polynomial coefficients to feedback parameters is formulated in order to place the system eigen values in the desired region. The feedback parameters determined from linearized model are tested on nonlinear model subjecting it to small disturbances and system faults to show the effectiveness of the controller designed by the proposed technique. The results obtained indicate that the controller presented improves the dynamic stability and system performances of conventionally controlled synchronous machine significantly.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.213-221
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• 2024

A family of sixth-order multiple-root solver have been developed and the special case of weight function is investigated. The dynamical analysis of selected iterative schemes with uniparametric polynomial weight function are studied using Möbius conjugacy map applied to the form ((z - A)(z - B))^m and the stability surfaces of the strange fixed points for the conjugacy map are displayed. The numerical results are shown through various parameter spaces.

• Structural Engineering and Mechanics
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• v.73 no.6
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• pp.685-698
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• 2020

The dynamic stability of a functionally graded polymer microbeam reinforced by graphene oxides subjected to a periodic axial force is investigated. The microbeam is assumed to rest on an elastic substrate and is subjected to various immovable boundary restraints. The weight fraction of graphene oxides nanofillers is graded across the beam thickness. The effective Young's modulus of the functionally graded graphene oxides reinforced composite (FG-GORC) was determined using modified Halpin-Tsai model, with the mixture rule used to evaluate the effective Poisson's ratio and the mass density. An improved third order shear deformation theory (TSDT) is used in conjunction with the Chebyshev polynomial-based Ritz method to derive the Mathieu-Hill equations for dynamic stability of the FG-GORC microbeam, in which the scale effect is taken into account based on modified couple stress theory. Then, the Mathieu-Hill equation was solved using Bolotin's method to predict the principle unstable regions of the FG-GORC microbeams. The numerical results show the effects of the small scale, the graphene oxides nanofillers as well as the elastic substrate on the dynamic stability behaviors of the FG-GORC microbeams.

• Journal of Pharmaceutical Investigation
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• v.20 no.2
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• pp.55-64
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• 1990

Soybean fatty acid, the largest byproduct in the production of soybean oil, was formulated for hand cream, oil in water emulsion base, to improve the suppleness and elasticity of skin. The stability of emulsion observed by a macroscopic method was used as a characteristic index for deciding an optimum formula of hand creams. The optimum formula of the most stable hand cream was obtained from polynomial regression equation, contour graphs and partial derivative graphs. The values of soybean fatty acid and stearyl alcohol in the obtained optimum formula were 9.75 and 14.75 w/w%, respectively, and sodium lauryl sulfate was not needed. Experimental value for the stability of hand cream prepared according to the optimum formula was 76,14 days, and the prediction value by computation method was 73.25 days. From the results of accelerated tests by elevated temperature, the stability of hand cream by optimum formula was 1.7 year at room temperature $(25^{\circ}C)$. The hand cream containing soybean fatty acid was found to be free of primary irritant substance to the skin by Draize technique.

• Structural Engineering and Mechanics
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• v.11 no.5
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• pp.565-574
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• 2001

Experimental investigation into the behaviour of half-scale brick masonry panels were conducted under cyclic loading normal to the bed joint and parallel to the bed joint. For each cycle, full reloading was performed with the cycle peaks coinciding approximately with the envelope curve. Unloading, however, was carried out fully to zero stress level and partially to two different stress levels of 25 percent and 50 percent of peak stress. Stability point limit exhibits a unique stress-strain curve for full unloading but it could not be established for partial unloading. Common point limit was established for all unloading-reloading patterns considered, but its location depends on the stress level at which unloading is carried to. Common point curves were found to follow an exponential formula, while residual strains versus envelope strains can be expressed by a polynomial function of a single term. The relation between residual strain and envelope strain can be used to determine the stress level at which deterioration due to cyclic loading began.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.657-670
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• 2015

In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.