• Journal for History of Mathematics
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• v.23 no.2
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• pp.89-99
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• 2010

Today linear algebra is one of compulsory courses for university mathematics by virtue of its theoretical fundamentals and fruitful applications. Vector theory and matrix theory constitute of main topics in linear algebra. In the present paper we consider the question which of the two topics is prior in teaching of linear algebra. We suggest that vector theory should be prior to matrix theory contrary to the historical order of them.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.2
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• pp.235-241
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• 2001

A crack with electrically conducting surfaces in a linear electrostrictive ceramic subjected to uniform electric fields is analyzed. Complete forms of electric fields and elastic fields for the crack are derived by using the complex function theory. The linear electromechanical theory predicts overlapping of the traction free crack surfaces. It is shown that the surfaces of the crack are contact near the crack tip. The contact zone size obtained on the basis of the linear dielectric theory for the conducting crack does not depend on the electric fields and depends on only the original crack and the material property for the linear electrostrictive ceramic.

• Structural Engineering and Mechanics
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• v.1 no.1
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• pp.87-102
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• 1993

A $C^{\circ}$ continuous finite element formulation of a higher order displacement theory is presented for predicting linear and geometrically non-linear in the sense of von Karman transient responses of composite and sandwich plates. The displacement model accounts for non-linear cubic variation of tangential displacement components through the thickness of the laminate and the theory requires no shear correction coefficients. In the time domain, the explicit central difference integrator is used in conjunction with the special mass matrix diagonalization scheme which conserves the total mass of the element and included effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the linear and geometrically non-linear responses are investigated. Numerical results for central transverse deflection, stresses and stress resultants are presented for square/rectangular composite and sandwich plates under various boundary conditions and loadings and these are compared with the results from other sources. Some new results are also tabulated for future reference.

• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.

• The Journal of Art Theory & Practice
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• no.7
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• pp.165-188
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• 2009

In the development of linear perspective, Brook Taylor's theory has achieved a special position. With his method described in Linear Perspective(1715) and New Principles of Linear Perspective(1719), the subject of linear perspective became a generalized and abstract theory rather than a practical method for painters. He is known to be the first who used the term 'vanishing point'. Although a similar concept has been used form the early stage of Renaissance linear perspective, he developed a new method of British perspective technique of measure points based on the concept of 'vanishing points'. In the 15th and 16th century linear perspective, pictorial space is considered as independent space detached from the outer world. Albertian method of linear perspective is to construct a pavement on the picture in accordance with the centric point where the centric ray of the visual pyramid strikes the picture plane. Comparison to this traditional method, Taylor established the concent of a vanishing point (and a vanishing line), namely, the point (and the line) where a line (and a plane) through the eye point parallel to the considered line (and the plane) meets the picture plane. In the traditional situation like in Albertian method, the picture plane was assumed to be vertical and the center of the picture usually corresponded with the vanishing point. On the other hand, Taylor emphasized the role of vanishing points, and as a result, his method entered the domain of projective geometry rather than Euclidean geometry. For Taylor's theory was highly abstract and difficult to apply for the practitioners, there appeared many perspective treatises based on his theory in England since 1740s. Joshua Kirby's Dr. Brook Taylor's Method of Perspective Made Easy, Both in Theory and Practice(1754) was one of the most popular treatises among these posterior writings. As a well-known painter of the 18th century English society and perspective professor of the St. Martin's Lane Academy, Kirby tried to bridge the gap between the practice of the artists and the mathematical theory of Taylor. Trying to ease the common readers into Taylor's method, Kirby somehow abbreviated and even omitted several crucial parts of Taylor's ideas, especially concerning to the inverse problems of perspective projection. Taylor's theory and Kirby's handbook reveal us that the development of linear perspective in European society entered a transitional phase in the 18th century. In the European tradition, linear perspective means a representational system to indicated the three-dimensional nature of space and the image of objects on the two-dimensional surface, using the central projection method. However, Taylor and following scholars converted linear perspective as a complete mathematical and abstract theory. Such a development was also due to concern and interest of contemporary artists toward new visions of infinite space and kaleidoscopic phenomena of visual perception.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.24-27
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• 1994

This paper develops a representation theory of linear systems by means of doubly coprime factorizations, and applies the theory to the simultaneous stabilization problem for a given set of linear systems.

• Nuclear Engineering and Technology
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• v.52 no.5
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• pp.947-955
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• 2020

Predicting the sloshing motion of a coolant during a seismic assessment of a rectangular spent fuel pool is of critical concern. Linear theory, which provides a simple analytical method, has been used to predict the sloshing motion in rectangular pools and tanks. However, this theory is not suitable for the high-frequency excitation problem. In this study, the authors developed a simple analytical method for predicting the sloshing motion in a rectangular pool for a wide range of excitation frequencies. The correlation among the linear theory parameters, influencing on excitation and convective waves, and the excitation frequency is investigated. Sloshing waves in a rectangular pool with several liquid heights are predicted using the original linear theory, a modified linear theory and computational fluid dynamics analysis. The results demonstrate that the developed method can predict sloshing motion over a wide range of excitation frequencies. However, the developed method has the limitations of linear solutions since it neglects the nonlinear features of sloshing motion. Despite these limitations, the authors believe that the developed method can be useful as a simple analytical method for predicting the sloshing motion in a rectangular pool under various external excitations.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.55.3-55.3
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• 2017

We present the preliminary result of our Lagrangian perturbation theory for the large-scale structure formation, in the presence of the cold dark matter (CDM) and the baryonic fluid. In the linear order, two mutually independent pseudo-particles can describe the evolution of density fluctuations and the accuracy of the calculation is better than the 4-mode (growing, decaying, streaming, compensated) Eulerian linear perturbation theory. In the $2^{nd}$ order, the separability of pseudo-particles is not as straightforward as in the linear order, and the related difficulty in developing the $2^{nd}$ order theory will also be presented.

• Publications of The Korean Astronomical Society
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• v.26 no.2
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• pp.55-70
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• 2011

Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.117-128
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• 1996

Complementation theory in krein spaces can be extended for any self-adjoint transformation. There is a close relation between Julia operators and linear systems. The theory of Julia operators can be used to construct distinct Krein spaces which are the state spaces of extended canonical linear systems with given transfer function.