• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.113-125
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• 2019

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.3
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• pp.59-63
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• 2008

A static load analysis of twin-screw kneaders is required not only for the dynamic analysis, but also because it is the basis of the stiffness and strength calculations that are essential for the design of bearings. In this paper, the static loads of twin-screw kneaders are analyzed, and a mathematical model of the force and torque moments is presented using a numerical integration method based on differential geometry theory. The calculations of the force and torque moments of the twin-screw kneader are given. The results show that the $M_x$ and $M_y$ components of the fluid resistance torque of the rotors change periodically in each rotation cycle, but the $M_z$ component remains constant. The axis forces $F_z$ in the female and male rotors are also constant. The static load calculated by the proposed method tends to be conservative compared to traditional methods. The proposed method not only meets the static load analysis requirements for twin-screw kneaders, but can also be used as a static load analysis method for screw pumps and screw compressors.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.257-279
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• 2023

This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium.

• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.675-696
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• 2009

In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.592-597
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• 2003

In this paper, some differential geometric conditions for the observer using a recurrent neural network are provided in terms of a stochastic nonlinear system control. In the stochastic nonlinear system, it is necessary to make an additional condition for observation of stochastic nonlinear system, called perfect filtering condition. In addition, we provide a observer using a recurrent neural network for the observation of a stochastic nonlinear system with the proposed observation conditions. Computer simulation shows that the control performance of the stochastic nonlinear system with a observer using a recurrent neural network satisfying the proposed conditions is more efficient than the conventional observer as Kalman filter

• Journal for History of Mathematics
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• v.18 no.2
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• pp.31-42
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• 2005

Renaissance is revival of the ancient Greek and Roman cultures. So, in Renaissance period, the artists began to study Euclidean geometry and then their mind was a spirit of experience and observation. These spirits is namely modernism. In other words, Renaissance was a dawn of modern times. In this paper, we notice modern spirits and ones social backgrounds. Differential and integral calculus was created by these modern spirits. And in art field, 'painter of light', 'artist of moment' appeared. Because in the 17th and 18th centuries, the intelligentsia researched for motions, speeds and lights.

• Journal of Korean Association for Spatial Structures
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• v.2 no.3 s.5
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• pp.115-122
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• 2002

It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.

• Journal for History of Mathematics
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• v.29 no.2
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• pp.103-143
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• 2016

We study the topics of the lectures in Analysis in 19th century at Ecole Polytechnique of France through the lists of the contents of the Cours d'Analyse by Cauchy, Sturm and Jordan, respectively and also we show how they stated the definitions of functions, continuity and limits in their Cours d'Analyse. Through this, we see that in 19th century, in France, analysis included differential and integral calculus, differential equations, variations and applications of these to differential geometry, and it was far from today's mathematical analysis.

• Particle and aerosol research
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• v.10 no.1
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• pp.33-43
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• 2014

A differential mobility analyzer (DMA) has been widely used as a standard tool for classifying nanoparticles with a certain size. More recently, several new types of DMA have been tested in an attempt to produce size-monodisperse nanoparticles. It is a bit surprise to see how simple the working theory of the DMA is. Although the theory was demonstrated quite successful, no one can guarantee whether the theory still works in another geometry of the DMA. In this regard, we first investigated the validity of the theory under various working conditions and then moved to check the validity upon minor change in its design. For the valid test, we compared the results with those obtained from a computational fluid dynamics.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.2 s.119
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• pp.185-193
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• 2007

This paper deals with the application of the numerical differentiation using the differential quadrature(DQ) in the curved member-like structural analysis. Derivative values of the geometry of structure are definitely needed for analyzing the structural behavior. For verifying the numerical differentiation using DQ, free vibration problems of arch are selected. Terms of curvature composed with the derivatives of arch geometry obtained herein are agreed quite well with exact values obtained explicitly. Natural frequencies subjected to terms of curvature obtained by DQ are agreed quite well with those in the literature. The numerical differentiation using DQ can be practically utilized in the structural analysis.