• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• Selected Papers of The Society of Naval Architects of Korea
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• v.2 no.1
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• pp.79-105
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• 1994

A ship in waves is suffered from the various wave loads that comes from its motion throughout its life. Because these loads are dynamic, the analysis of a ship structure must be considered as the dynamic problem precisely. In the rationally-based design, the dynamic structural analysis is carried out using dynamic wave loads provided from the results of the ship motion calculation as a rigid body. This method is based on the linear theory assumed low wave height and small amplitude of motion. But at the rough sea condition, high wave height, compared with ship's depth, induce the large ship motion, so the ship section configuration under waterline is rapidly changed at each time. This results in a non-linear problem. Considering above situation in this paper, a strength analysis method is introduced for the hull girder among waves considering non-linear hydrodynamic forces. This paper evaluates the overall or primary level of the ship structural dynamic loading and dynamic response provided from the non-linear wave forces, and bottom flare impact forces by momentum slamming theory. For numerical calculation a ship is idealized as a hollow thin-walled box beam using thin walled beam theory and the finite element method is used. This method applied to a 40,000 ton double hull tanker and attention is paid to the influence of the response of the ship's speed, wave length and wave height compared with the linear strip theory.

• Steel and Composite Structures
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• v.42 no.5
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• pp.711-722
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• 2022

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.123-139
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• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential equations and general boundary conditions. The basic new idea of this paper is to introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.543-559
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• 2002

In this paper we formulate the linear theory for compressible fluids in cylindrical geometry with small perturbation at the material interface. We derive the first order equations in the smooth regions, boundary conditions at the shock fronts and the contact interface by linearizing the Euler equations and Rankine-Hugoniot conditions. The small amplitude solution formulated in this paper will be important for calibration of results from full numerical simulation of compressible fluids in cylindrical geometry.

• The Mathematical Education
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• v.42 no.4
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• pp.481-501
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• 2003

The main purpose of this work is to propose programs of algebra courses for the department of mathematics education of teacher training universities. Set Theory, Linear Algebra, Number Theory, Abstract Algebra I, Abstract Algebra II, and Philosophy of Mathematics for School Teachers are discussed in this article.

• Journal of Magnetics
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• v.21 no.1
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• pp.125-132
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• 2016

High gradient magnetic separation (HGMS) is the most commonly used magnetic cell separation technique in biomedical science. However, parameters determining target cell capture efficiencies in HGMS are still not well understood. This limitation leads to loss of information and resources. The present study develops a bead-capture theory to predict capture efficiencies in HGMS. The theory is tested with CD3- and CD14-positive cells in combination with paramagnetic beads of different sizes and a generic immunomagnetic separation system. Data depict a linear relationship between normalized capture efficiency and the bead concentration. In addition, it is shown that key biological functions of target cells are not affected for all bead sizes and concentrations used. In summary, linear bead-capture theory predicts capture efficiency ($E_t$) in a highly significant manner.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.18 no.4
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• pp.83-87
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• 2004

In this paper, an electrical equivalent circuit is derived by solving system equations. A frequency characteristics graph is calculated and the characteristics curve of the linear Actuator Model System are simulated by the Matlab program The frequency characteristics of a linear actuator are analyzed on the structure of the linear Actuator Model System This paper proposed and analyzed the linear Actuator Model(LAM) by using Matlab program with linear actuator was verified computer simulation based on the energy conversion theory.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.609-619
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• 1999

We give a mathematically rigorous description of the recently popular latent semantic indexing (LSI) method in text information retrieval theory. Also, a related problem of finding a document ranking function in linear relevance feedback is discussed.

• Smart Structures and Systems
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• v.18 no.2
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.