• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.999-1011
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• 2009

In this paper, we are concerned with the following eigenvalue problems of m-point boundary value problem for p-Laplacian dynamic equation on time scales $(\varphi_p(u^{\Delta}(t)))^\nabla+{\lambda}h(t)f(u(t))=0,\;t\in(0,T)$, $u(0)=0,\varphi_p(u^{\Delta}(T))=\sum\limits_{i=1}^{m-2}a_i\varphi_p(u^{\Delta}(\xi_i))$, where $\varphi_p(u)=|u|^{p-2}$u, p > 1 and $\lambda$ > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solution and nonexistence are obtained for $\lambda$ evaluated in different intervals. Our work develop and improve many known results in the literature even for the continual case. In doing so the usual restriction that $f_0=lim_{u{\rightarrow}0}+f(u)/\varphi_p(u)$ and $f_\infty = lim_{u{\rightarrow}{\infty}}f(u)/\varphi_p({u})$ exist is removed. As an applications, an example is given to illustrate the main results obtained.

• Wind and Structures
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• v.14 no.4
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• pp.359-381
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• 2011

This paper deals with the flutter instability problem of flexible bridge decks in the framework of bimodal-coupled aeroelastic bridge system analysis. Based on the analysis of coefficients of the polynomials deduced from the singularity conditions of an integral wind-structure impedance matrix, a set of simplified formulations for calculating the critical wind velocity and coupled frequency are presented. Several case studies are discussed and comparisons with available approximated approaches are made and presented, along with a conventional complex eigenvalue analysis and numerical results. From the results, it is found that the formulas that are presented in this study are applicable to a variety of bridge cross sections that are not only prone to coupled-mode but also to single-mode-dominated flutter.

• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.601-610
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• 2024

Free vibration of layered conical shell frusta of thickness filled with fluid is investigated. The shell is made up of isotropic or specially orthotropic materials. Three types of thickness variations are considered, namely linear, exponential and sinusoidal along the radial direction of the conical shell structure. The equations of motion of the conical shell frusta are formulated using Love's first approximation theory along with the fluid interaction. Velocity potential and Bernoulli's equations have been applied for the expression of the pressure of the fluid. The fluid is assumed to be incompressible, inviscid and quiescent. The governing equations are modified by applying the separable form to the displacement functions and then it is obtained a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by cubic and quintics splines along with the boundary conditions to get generalized eigenvalue problem. The generalized eigenvalue problem is solved numerically for frequency parameters and then associated eigenvectors are calculated which are spline coefficients. The vibration of the shells with the effect of fluid is analyzed for finding the frequency parameters against the cone angle, length ratio, relative layer thickness, number of layers, stacking sequence, boundary conditions, linear, exponential and sinusoidal thickness variations and then results are presented in terms of tables and graphs.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.31-37
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• 2002

In this paper, we find explicitly the eigenvalues and the eigenfunctions of Laplace operator on a triangle domain with a mixed boundary condition. We also show that a weaker form of the principle of spatial averaging holds for this domain under suitable boundary condition.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.267-277
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• 2011

This paper is concerned with eigenvalues of second-order vector equations on time scales with boundary value conditions. Properties of eigenvalues and matrix-valued solutions are studied. Relationships between eigenvalues of different boundary value problems are discussed.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.411-418
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• 2018

In this paper, we prove the discrete compactness property for Kim-Kwak finite element spaces of any order under a weak quasi-uniformity assumption.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.83-85
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• 1995

A technique for power system' stabilization is presented using the variable structure control theory. The selection problem of the proper switching vector is very important subject for a design of the variable structure controller. In this paper, the switching vector is selected by desired eigenvalues allocation. and these desired eigenvalues are determined by eigenvalue assignment. Simulation results show that eigenvalue allocation variable structure stabilizer yields better dynamic performance than the others (conventional PSS, optimal linear stabilizer) and is robust to wide variations of the system parameters.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.637-654
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• 2011

The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh's statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, "new" modes are found to be a combination of the subsystem's modes (two rotations, traslation) and the bare plate's modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate's modes enable distinct motions of the 3-DOF system contributing differently to the "new' modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.

• Korea-Australia Rheology Journal
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• v.21 no.2
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• pp.143-146
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• 2009

Breakthrough of high Weisenberg number problem is related with keeping the positive definiteness of the conformation tensor in numerical procedures. In this paper, we suggest a simple method to preserve the positive definiteness by use of vector decomposition of the conformation tensor which does not require eigenvalue problem. We also derive the constitutive equation of tensor-logarithmic transform in simpler way than that of Fattal and Kupferman and discuss the comparison between the vector decomposition and tensor-logarithmic transformation.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1045-1058
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• 2000

In usual synchronous parallel computing, workload balance is a crucial factor to reduce idle times of some processors that have finished their jobs earlier than others. However, it is difficult to achieve on a heterogeneous workstation clusters where the available computing power of each processor is unpredictable. As a way to overcome such a problem, the idea of asynchronous methods has grown out and is being increasingly used and studied, but there is none for eigenvalue problems yet. In this paper, we suggest a new asynchronous method to solve some singular matrix problems, that can also be used for finding a certain eigenvector of some matrices.