• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.1-17
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• 2024

The boundary conditions $\tilde{P}_0$ and $\tilde{P}_1$ were introduced in [5] by using the Hodge decomposition on the de Rham complex. In [6] the Atiyah-Bott-Lefschetz type fixed point formulas were proved on a compact Riemannian manifold with boundary for some special type of smooth functions by using these two boundary conditions. In this paper we slightly extend the result of [6] and give two examples showing these fixed point theorems.

• Structural Engineering and Mechanics
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• v.25 no.6
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• pp.717-732
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• 2007

A formula to approximate the fundamental period of a fixed-free mass-spring system with varying mass and varying stiffness is formulated. The formula is derived mainly by taking the dominant parts from the general form of the characteristic polynomial, and adjusting the initial approximation by a coefficient derived from the exact solution of a uniform case. The formula is tested for a large number of randomly generated structures, and the results show that the approximated fundamental periods are within the error range of 4% with 90% of confidence. Also, the error is shown to be normally distributed with zero mean, and the width of the distribution (as measured by the standard deviation) tends to decrease as the total number of discretized elements in the system increases. Other possible extensions of the formula are discussed, including an extension to a continuous cantilever structure with distributed mass and stiffness. The suggested formula provides an efficient way to estimate the fundamental period of building structures and other systems that can be modeled as mass-spring systems.

• East Asian mathematical journal
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• v.36 no.5
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• pp.593-604
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• 2020

Let the circle act on a compact oriented manifold with a discrete fixed point set. At each fixed point, there are positive integers called weights, which describe the local action of S¹ near the fixed point. In this paper, we provide the author's original proof that only uses the Atiyah-Singer index formula for the classification of the weights at the fixed points if the dimension of the manifold is 4 and there are at most 4 fixed points, which made the author possible to give a classification for any finite number of fixed points.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.3
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• pp.87-94
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• 2013

The progress that becomes a basis for measuring the outcome of project is a core of project control. Follow-up corrective actions are determined depending on the degree of their differences. The methods of measuring the project progress have been developed though a variety of research and many were verified through the cases. Among such methods, this study selected Start/Finish method and Fixed Formula method. In order to check the limitations of the progress utilized in the two methods, the study compared their progresses to the progress of Percentage Complete method and analyzed the differences shown in their actual applications. Through this, it suggested the forms and scale of the projects appropriate to the application of Fixed Formula method. As for the research progress method, the study first generated a number of virtual project schedules for the establishment of an analysis model. These project schedules were varied in a way that they had different project periods and the number of different activities. The study also generated numerous project schedules for difference test. After establishing a virtual schedule plan by the scale of projects, it measured their progresses by period, analyzed the differences and repeated this procedure to obtain the results.

• Journal of Wetlands Research
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• v.13 no.3
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• pp.677-686
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• 2011

This study proposes a formula to calculate length of river bed protection through experimental research and an experimental plant has been installed to investigate the parameters which influence the length of scouring in the river after overflowing the weir. Through hydraulic experiments, the critical velocity, difference of water level between upstream and downstream and height of weir have been selected as independent variables. And new formula to calculate a length of river bed protection is suggested as the result of this study in the consideration of complex weir that consists of movable and fixed weir. The new formula is verified through additional experiments. Results of this study can be used for weir structures' construction and maintenance plans.

• Journal of Ocean Engineering and Technology
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• v.16 no.5
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• pp.49-55
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• 2002

The compression anchor is characterized by decrement of progressive failure, simple site work, economy and durability compared with tension anchor. In this paper, compression anchor is analysed through the laboratory element tests. The formula to be estimate the grout strength in fixed part of compression anchor and the effective reinforcement method for several types of soil were suggested. The following conclusions were made from this study : (1) A formula, which is able to calculate the grout strength in the fixed part of the compression anchor, is suggested. (2) The strength increment ratios( $R_{si}$) are 100％, 132％, 147％, 217％ according to the reinforcement method of grout. The reinforcement method is Non, Outside spiral, Inside-Outside spiral, Steel pipe, respectively. (3) The strength increment ratios( $R_{si}$) by reinforcing can be 8.23 times the strength increment effect according to the reinforcement types and ground confining pressure. (4) The steel pipe reinforcement is most effective in decomposed soil while, in the case of hard rock ground, high confining pressure is exerted on the grout, so there is no need to use reinforcements.

• Journal of Communications and Networks
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• v.9 no.2
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• pp.159-166
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• 2007

In this paper, we propose an efficient and robust interference mitigation technique based on a nullsteering multi-user multiple-input multiple-output (MU-MIMO) spatial division multiple access (SDMA) scheme for frequency sharing between IMT-advanced and fixed satellite service (FSS) in the 3400-4200 and 4500-4800 MHz bands. In the proposed scheme, the pre-existing precoding matrix for SDMA unitary precoded (UPC) MIMO proposed by the authors is modified to construct nulls in the spatial spectrum corresponding to the direction angles of the victim FSS earth station (ES). Furthermore, a numerical formula to calculate the power of the interference signal received at the FSS ES when IMT-Advanced base stations (BS) are operated with the interference mitigation technique is presented. This formula can be derived in closed form and is simply implemented with the help of simulation, resulting in significantly reduced time to obtain the solution. Finally, the frequency sharing results are analyzed in the co-channel and adjacent channel with respect to minimum separation distance and direction of FSS earth station (DOE). Simulation results indicate that the proposed mitigation scheme is highly efficient in terms of reducing the separation distance as well as robust against DOE estimation errors.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.3
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• pp.366-377
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• 2016

This paper presents a vision-based guidance method that allows a fixed-wing aircraft to orbit around a target at a given radius. The guidance method uses a simple formula that regulates a relative side-bearing angle estimated by a vision system. The global asymptotic stability of the associated guidance law is demonstrated, and a linear analysis is performed to facilitate the proper selection of the relevant control parameters. A flight experiment is presented to demonstrate the feasibility and performance of the proposed guidance method.

• Proceedings of the KIEE Conference
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• 1994.11a
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• pp.120-123
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• 1994

The purpose of this paper is to describe the mutual inductance between two non-coaxial circular coils in coil gun. As being in many electromagnetic applications, one of them is fixed and the other one is moving and, being not supported, its axis may not coincide with the axis of the fixed coil. This paper presents a method for the calculation of the mutual inductance in case of non-coaxial coupled coils, the characteristics of this inductance and experimental results. For the computation, the complete elliptic integrals formula and mesh matrix technique were introduced. This method enables accurate results from relatively simple procedure and calculation program.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.