• Journal for History of Mathematics
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• v.31 no.5
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• pp.211-222
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• 2018

This paper surveys the theory of symmetry group of differential equations. A proof of the simplest version of the Noether's theorem on conservation laws has been presented with examples in the classical mechanics. As a new approach to the conservation laws the theory of characteristic cohomology due to S. H. Wang and others has been presented.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.869-882
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• 2023

In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.517-561
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• 2003

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in $\mathbb{C}$. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.787-813
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• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.669-690
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• 1998

In this paper we develop a new theory of adjoint and symmetric method in the class of general implicit one-step fixed-stepsize methods. These methods arise from simple and natral def-initions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for meth-ods having these properties and show in particular that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition we give a very simple test to identify the symmetric methods in practice.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.293-298
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• 2005

We calculate the coordinates of an axisymmetric nozzle with a central body. This nozzle ensures a transonic flow with a plane sound surface, which is orthogonal to the symmetry axis and has a wall kink at the sonic point, The Chaplygin transformation in the subsonic part of the flow leads the Dirichlet problem for a system of nonlinear equations. The definition domain of the solution in the velocity-hodograph plane is taken as a rectangle. This enables one to obtain the nozzle with a monotonic distribution of velocity along its subsonic part. In the nonlinear differential equation, the linear Chaplygin operator for plane flows is separated, which allows the iterative calculation of the solution. The supersonic part of the nozzle is calculated under the assumption that the flow at the nozzle exit is uniform and parallel to the symmetry axis; i.e., the supersonic jet outflows to the submerged space with the same pressure. The calculation is performed by the characteristic method. The exact solution of Tricomi equation for near-sonic flows with the straight sonic line is used to 'move away' the sound plane. The velocity distribution alone the supersonic part of the nozzle is also monotonic, which ensures the absence of the boundary-layer separation and, therefore, the adequacy of the ideal-gas model. calculations show that the flow in the supersonic part of the nozzle is continuous (compression shocks are absent)

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.12
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• pp.1338-1346
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• 2009

We present a one-dimensional annular plate element with which the in-plane vibration of full disks can be analyzed efficiently and accurately by using the FEM. Its elementary mass matrix and stiffness matrix are derived, respectively, from the virtual work by effective forces and the virtual strain energy. The static deformation modes obtained from an integration of the differential equilibrium equations of the annular plate are used as interpolation functions of the one-dimensional annular plate element. The in-plane natural vibration characteristics of a 2-step full disk and a uniform full disk are analysed. Its results are compared with the results obtained by utilizing two-dimensional 8-node quadrilateral plane elements and cyclic symmetry of the disk. And also, by comparing with the theoretical results of previous researchers, the efficiency and accuracy of the presented element are verified.

• Journal of Korean Philosophical Society
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• v.105
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• pp.269-290
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• 2008

The purpose of this paper is to explore the possibility of backwards causation. For study, this paper was divided into four views as follows: The first view was sometimes suggested by the people such as M. Dummett who distinguished observers from behaviors. According to observers' view, backwards causation is impossible, whereas behaviors' view possible. However, in a real or genuine sense, it is incorrect for us to argue for impossibility of backwards causation from the observer aspect. The second view was supported by J. H. Schmidt. He analyzed the possibility of backwards causation in terms of macro and micro level analysis about the causal events. According to micro level analysis, backwards causation is possible, but macro level analysis impossible. Usually the latter makes the former something miraculous. Under the macro level analysis, backwards causation, at first, seems to be miraculous phenomena which belongs to the micro level analysis. The third view had to do with physical equation, and the fourth view physical phenomena, respectively. John Earman argued for the backwards causation by the transformation from Lorentz­-Dirac equation to a second-order integro-differential one in the field of electrodynamic acceleration. His argument was criticized because of his misunderstanding about the relationship between two equations. On the other hand, Phil Dowe defended a version of Reichenbach's own theory about the direction of causation founded on the fork asymmetrical causal relation. However his view was different from Reichenbach's because the former defended the backwards causation model of Bell phenomena in quantum mechanics. On the contrary, Reichenbach put stressed on the priority of cause in the causal process. Subjectivism has recently been defended by H. Price, under the label of perspectivism. According to him, in a certain sense causal asymmetry is not in the world, but is rather a product of our own asymmetric perspective on the world. He also suggested causal net, the symmetry of microphysics, and so on. As mentioned above, there are many kind of suggestions of backwards causation. However none of them replaced objectively the main streams of the direction of causal process. The main stream has been usually defended by pragmatical ground. That is, effects do not precede their causes although causes cannot be without their effects.