• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1237-1248
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• 2009

The domain of attraction of a nonlinear differential equations is the region of initial points of solution tending to the equilibrium points of the systems as the time going. Determining the domain of attraction is one of the most important problems to investigate nonlinear dynamical systems. In this article, we first present two algorithms to determine the domain of attraction by using the moment matrices. In addition, as an application we consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method, and also estimate the domain of attraction by using the algorithms.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.137-149
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• 2020

Let γ⁽ⁿ⁾ ≡ {γ_ij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ⁽ⁿ⁾. For an odd number n, it is known that γ⁽ⁿ⁾ has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4E
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• pp.20-25
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• 1999

To get accurate natural frequencies of an engine crankshafts, finite element equations of motion are developed, taking real geometries of the shaft into account. For the crankshaft with wide crank webs, a specialized rotating web element is developed. This includes the effects of rotary inertia, gyroscopic moment, and shear. After the finite element equations are constructed, eigenvalues are extracted from the system equations to get natural frequencies, based on the Sturm sequence method which exploits the banded forms of the system matrices to reduce computations. The scheme developed can be used for the free vibration analysis of any type of spinning structures which include skew symmetric gyroscopic moment matrix in the system matrices. The results are compared with experimental data in order to confirm the study.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.723-747
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• 2005

In this paper, we consider the quartic moment problem suggested by Curto-Fialkow[6]. Given complex numbers $\gamma{\equiv}{\gamma}^{(4)}\;:\;{\gamma00},\;{\gamma01},\;{\gamma10},\;{\gamma01},\;{\gamma11},\;{\gamma20},\;{\gamma03},\;{\gamma12},\;{\gamma21},\;{\gamma30},\;{\gamma04},\;{\gamma13},\;{\gamma22},\;{\gamma31},\;{\gamma40}$, with ${\gamma00},\;>0\;and\;{\gamma}_{ji}={\gamma}_{ij}$ we discuss the conditions for the existence of a positive Borel measure ${\mu}$, supported in the complex plane C such that ${\gamma}_{ij}=\int\;\={z}^i\;z^j\;d{\mu}(0{\leq}i+j{\leq}4)$. We obtain sufficient conditions for flat extension of the quartic moment matrix M(2). Moreover, we examine the existence of flat extensions for nonsingular positive quartic moment matrices M(2).

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.949-970
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• 2007

By considering a bridge between Bram-Halmos and Embry characterizations for the subnormality of cyclic operators, we extend the Curto-Fialkow and Embry truncated complex moment problem, and solve the problem finding the finitely atomic representing measure ${\mu}$ such that ${\gamma}_{ij}={\int}\bar{z}^iz^jd{\mu},\;(0{\le}i+j{\le}2n,\;|i-j|{\le}n+s,\;0{\le}s{\le}n);$ the cases of s = n and s = 0 are induced by Bram-Halmos and Embry characterizations, respectively. The former is the Curto-Fialkow truncated complex moment problem and the latter is the Embry truncated complex moment problem.

• Bulletin of the Society of Naval Architects of Korea
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• v.12 no.1
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• pp.23-30
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• 1975

Because of the simplicity in analysis and design of steel structure, the connections of members are assumed either as perfectly hinged or rigidly fixed. However, a more economical design would result if the effect of restraint in connections were included in analyzing frame structure. From this point of view, stiffness matrices for member with bracketed connections are presented in the form of the stiffness matrices for member with variable moment of inertia, modified by a correction matrix, whose elements are functions of fixity factors of the connections. To obtain fixity factors, the displacements and stress distribution of bracketed connections are investigated by using of the degital computer program, which have been developed to make computing time shorten and the round off errors smaller. The relationship of moments and slip angle in bracketed connections are presented in the form of curves, which can be used in establishing a stiffness matrices for member with bracketed connections.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.3
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• pp.337-344
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• 2000

The wavelet analysis technique is applied in the spectral domain to efficiently represent the multi-scale features of the impedance matrices. In this scheme, the 2-D quadtree decomposition (applying the wavelet transform to only the part of the matrix) method often used in image processing area is applied for a sparse moment matrix. CG(Conjugate-Gradient) method is also applied for saving memory and computation time of wavelet transformed moment matrix. Numerical examples show that for rectangular cylinder case the non-zero elements of the transformed moment matrix grows only as O($N^{1.6}$).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1042-1048
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• 2007

This work analytically investigated the radiated noise of a helical gear-housing system due to the excitation of helical gears. The helical gears were modeled as a 12-degree of freedom mass-spring-damper system; the shaft was modeled as a rod, a beam, and a torsional shaft; and the gear housing was modeled as a clamped circular plate with viscous damping. The modeling of this system used transfer matrices for helical gears, shafts, and bearings. Damping for both the bearings and the plate were obtained by modal testing. For the evaluation of noise, sound pressure from the plate due to the force and the moment in both radial and tangential directions was analytically derived by the Rayleigh integral. The analytical derivation and parameters from the experiment were applied to an analysis of noise for the two sets of helical gears with differing gear ratios. The analysis showed that the moment excitation in both helical gears contributed more to the noise of the plate than axial force excitation.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.586-589
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• 2004

A numerical algorithm using the Method of Moments (MoM) is introduced to compute precisely the scattering matrices of very thin deciduous leaves in this paper. At first, a dyadic Green's function was formulated and an integral equation for a volumetric current distribution in a lossy dielectric body. Then, the MoM was applied to the scattering problem with a specific technique to handle the numerical poles. The accuracy of the numerical technique was verified by examining the technique with various ways, and used to examine the validity regions of the classical analytical models.

• Journal of Soil and Groundwater Environment
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• v.16 no.3
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• pp.3-9
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• 2011

Partitioning tracers have been used with non-partitioning, inert tracer such Br, for detection, estimation, and monitoring of remediation performance of the subsurface contaminated with nonaqueous phase liquids (NAPLs). Various partitioning tracers with different partition coefficients between aqueous and nonaqueous phase liquids can be used to determine the hydraulic conductivity, dispersivity, and residual mass of NAPLs in the subsurface soil matrices. Temporal moment-generating equations were used to analyze the field pilot-scale test results. The pilot-scale tests included conservative tracer tests and partitioning tracer tests. Analyses of nonaqueous phase liquid distribution and characteristics of groundwater bearing soil media were performed.