• The Mathematical Education
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• v.13 no.2
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• pp.6-10
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• 1974

We consider 'ordinary' graphs: that is, finite undirected graphs with no loops or multiple edges. An intersection representation of a graph G is a function r from V(G), the set of vertices of G, into a family of sets S such that distinct points $\chi$$_{\alpha}$ and $\chi$$_{\beta}$/ of V(G) are. neighbors in G precisely when ${\gamma}$($\chi$$_{\alpha}$)∩${\gamma}$($\chi$$_{\beta}$/)$\neq$ø, A graph G is a rigid circuit grouph if every cycle in G has at least one triangular chord in G. In this paper we consider the main theorem; A graph G has an intersection representation by arcs on an acyclic graph if and only if is a normal rigid circuit graph.uit graph.d circuit graph.uit graph.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.2
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• pp.95-107
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• 1989

This paper proposes a realization method of multidimensional digital filters that has high modularity, regularity and parallelism enjoying the attributes for efficient VLSI implementation. The method shows that multidimensional transfer functions can be treated as two-dimensional transfer functions modifying the decomposition method of multidimensional transfer functions proposed by Venetsanopoulos etal, and then be displayed by multiplications and additions of one-dimensional transfer functions by applying the griangular decomposition theorem to the coefficient matrices of the two-dimensional transfer functions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.2
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• pp.145-152
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• 2009

In this paper, dynamic instability of plane membrane structures under wind action has been studied. The key to solving the governing equations of membrane structures under wind action is how to obtain the air pressure on membrane. Based on Bernoulli's theorem, fluid pressure has a certain relationship with velocity potential. Velocity potential could be solved according to thin aerofoil theory, where air around the membrane is regarded as a sheet of vortices. In this paper, we take advantage of the most commonly used three-node triangular membrane element and weighted residual-Galerkin method to obtain the determining equation for stability evaluation. Square and rectangular membrane structures are studied. The influence of initial prestressing force and wind direction towards critical wind velocity are also analyzed in this paper.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.1-16
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• 2007

In order to generalize theory of series in Iksan(翼算), we introduce a concept of double sequence of partial sums and elementary double sequence of partial sums, which play a dominant role in the study of double sequences of partial sums. We introduce a concept of finitely generated double sequence of partial sums and find a necessary and sufficient condition for those double sequences. Finally we prove a multiplication theorem for tetrahedral numbers and for 4 dimensional tetrahedral numbers.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2218-2229
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• 2006

A conservative finite-volume numerical method for unstructured grids with the cell-centered method has been developed for computing flow and heat transfer by combining the attractive features of the existing pressure-based procedures with the advances made in unstructured grid techniques. This method uses an integral form of governing equations for arbitrary convex polyhedra. Care is taken in the discretization and solution procedure to avoid formulations that are cell-shape-specific. A collocated variable arrangement formulation is developed, i.e. all dependent variables such as pressure and velocity are stored at cell centers. For both convective and diffusive fluxes the forms superior to both accuracy and stability are particularly adopted and formulated through a systematic study on the existing approximation ones. Gradients required for the evaluation of diffusion fluxes and for second-order-accurate convective operators are computed by using a linear reconstruction based on the divergence theorem. Momentum interpolation is used to prevent the pressure checkerboarding and a segregated solution strategy is adopted to minimize the storage requirements with the pressure-velocity coupling by the SIMPLE algorithm. An algebraic solver using iterative preconditioned conjugate gradient method is used for the solution of linearized equations. The flow analysis code (PowerCFD) developed by the present method is evaluated for its application to several 2-D structured-mesh benchmark problems using a variety of unstructured quadrilateral and triangular meshes. The present flow analysis code by using unstructured grids with the cell-centered method clearly demonstrate the same accuracy and robustness as that for a typical structured mesh.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.2
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• pp.137-142
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• 2017

Recently, the reduction of vehicle weight has been increasingly studied, in order to enhance the fuel efficiency of passenger cars. In particular, the seat frame is being studied actively, owing to considerations of driver safety from external impact damage. Therefore, this study focuses on high strength steel sheet (SPFC980)/polymer heterojunction hybrid materials, and their performance in regards to impact energy absorption. The ratio of impact energy absorption was observed to be relatively higher in the SPFC980/polymer hybrid materials under the impact load. This was found by calculating the equivalent flexural rigidity, which is the bending effect, according to the Castigliano theorem. An efficient wire-web structure was investigated through the simulation of different wire-web designs such as triangular, rectangular, octagonal, and hexagonal structures. The hexagonal wire-web structure was shown to have the least impact damage, according to the simulations. This study can be utilized for seat frame design for passengers' safety, owing to efficient impact absorption.

• Ocean and Polar Research
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• v.42 no.1
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• pp.77-88
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• 2020

This paper presents the coordinate systems used for trawl doors modeling, and provides matrix equations of connection between these systems. The projections of the forces acting on the door into axes of various coordinate systems were obtained, which were used in the door equilibrium equations. Six equilibrium conditions for the door as a solid were obtained: formulas that allow for the door area in plan to be determined; its weight in water; its mass; three moment equations for determining the position of the warp and backstrops fastening points to the door with triangular and quadrangular backstrop arrangements. It was found that the moment equilibrium equations of trawl doors are generally incompatible, which was not found by any of the authors who have previously conducted research into trawl doors. Using the Kronecker-Capelli theorem, the compatibility equation is obtained. This equation includes the coordinates of the backstrop fastening points to the door, which means that these points cannot be randomly selected. The technique of determining the warp and backstrops' fastening points position to the door is described. Conditions of directional (by angle of attack) and roll (in angle of roll) stability of the doors' equilibrium are presented. The equations presented in this paper comprise a mathematical model that allows, when designing the doors, to select optimal parameters, as well as to carry out adjustments for trawling purposes to ensure the stable movement of the doors and the entire trawl system.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.12-18
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• 1991

Three-dimensional nonlinear sloshing effects due to tank motions are simulated by solving boundary value problem using the panel method based on boundary integral technique. While Shinkai used boundary elements on which source strengths vary linearly between nodes, the source of constant strength is distributed on each triangular panel in the present study. The source strength at each time step is determined by solving the Fredholm integral equation of the second kind obtained from Green's theorem. To avoid cumulative numerical errors as time elapses, Adam-Bashforth-Moulton method is employed. Numerical examples for the case of partially filled spherical tank on board oscillating in harmonic sway mode or pitch mode are solved. The elevation of the free surface is compared with the result by Shinkai and confirmed in good agreement during early time. The input and the output energy are comparatively evaluated to check the overall accuracy of the present numerical scheme. Although some leakage of energy are found as time marches, it is plausible when we take into account nonlinearities of the problem and the number of panels of the model.