• East Asian mathematical journal
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• v.32 no.5
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• pp.717-728
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• 2016

In this paper, we give a necessary and sufficient condition for an essential simple loop on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a 2-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.673-683
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• 2009

We point out: to make Hermtian matrices A and B satisfy Styan matrix inequality, the condition "positive definite property" demanded in the present literatures is not necessary. Furthermore, on the premise of abandoning positive definite property, we derive Styan matrix inequality of Hadamard product for inverse Hermitian matrices and the sufficient and necessary conditions that the equation holds in our paper.

• Journal of the Korean Society of Safety
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• v.8 no.4
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• pp.73-81
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• 1993

In recent years, mould industry in machining requires to increase machining productivity and to reduce costs, To adapt this trend it is necessary to optimize machine condition, Even though many researches in this area introduced various way to set the optimal condition, still there are not enough. Therefore this research was done to select the optimal cutting condition for industry, and to develop the computer program to select the optimal cutting condition automatically. The result of this research will contribute to increase machining productivity of various mould companies with the automatic selection of optimal cutting condition.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.327-332
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• 2007

A variational inequality defined by the second-order cone is considered, and it is shown that a necessary and sufficient condition for a solution of the variational inequality holds under some regularity condition.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.377-385
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• 2000

In this paper we find a sufficient condition to guarantee the existence of pure-strategy equilibria in matrix games. In the process of formulating our condition, the alternative theorem of Farkas is used. The formulated condition is necessary and sufficient to the existence of pure-strategy equilibria in undominated matrix games.

• KCID journal
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• v.13 no.2
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• pp.223-235
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• 2006

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.2
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• pp.273-284
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• 2015

The feasibility conditions of interference alignment (IA) are analyzed for reverse duplex systems, in which one cell operates as downlink (DL) while the other cell operates as uplink (UL) assuming one-sid base station (BS) cooperation. Under general multiple-input and multiple-output (MIMO) antenna configurations, a necessary condition and a sufficient condition for one-shot linear IA are established, i.e., linear IA without symbol or time extension. In several example networks, optimal sum degrees of freedom (DoF) is characterized by the derived necessary condition and sufficient condition. For some special class of networks, a sufficient condition is established in a more compact expression, which also yields the necessary and sufficient condition. Simulation results demonstrate that the proposed IA does not only achieve larger DoF but also significantly improves the sum rate in the practical signal-to-noise ratio (SNR) regime.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.268-275
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• 2003

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. The dynamic loads are often transformed into static loads by dynamic factors, design codes, and etc. Therefore, the optimization results can give inaccurate solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple leading conditions which are not costly to include in modern structural optimization. In this research, it is mathematically proved that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition. At first, the solution of the new algorithm is mathematically obtained. Using the termination criteria, it is proved that the solution satisfies the Karush-Kuhn-Tucker necessary condition of the original dynamic response optimization problem. The application of the algorithm is discussed.

• International Journal of Highway Engineering
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• v.19 no.3
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• pp.19-30
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• 2017

PURPOSES : This study proposes the road asset valuation approach using alternative depreciation methods. It has become necessary to have asset management system according to the adoption of accrual basis accounting for governmental financial reporting and the amendment of the road act. Therefore, it is very important to analyze the effect of depreciation methods on road asset value as a basic research for road asset management system. METHODS : The Ministry of Strategy and Finance (MOSF) has mainly performed road asset valuation based on Write down Replacement Cost and Straight Line depreciation method. This study suggests some appropriate asset valuation methods for road assets through case analysis using three depreciation methods: Consumption-based depreciation method, Condition-based depreciation method, and Straight Line depreciation method. A road asset valuation data of national highway route 1 (year 2014) is used to analyze the effect of three depreciation methods on the road asset value. Road assets include land and structures (pavement, bridge, and tunnel). This study mainly focuses on structures such as bridges and tunnels, because according to governmental accounting standards, land and road pavement assets do not depreciate. RESULTS : The main results of this study are as follows. Firstly, overall asset value of national highway route 1 was estimated at 6.97 trillion KRW when MOSF's method (straight-line depreciation method) is applied. Secondly, asset value was estimated at 4.85 trillion KRW on application of consumption-based depreciation method. Thirdly, asset value was estimated at 4.37 trillion KRW when condition-based depreciation method is applied. Therefore, either consumption-based or condition-based depreciation methods would be more appropriate than straight-line depreciation method if we can use the condition data of road assets including land that are available in real time. CONCLUSIONS : Since road assets such as pavements, bridges, and tunnels have various patterns of deterioration and condition monitoring period, it is necessary to consider a specific valuation method according to the condition of each road asset. Firstly, even though road pavements do not depreciate, asset valuation through condition-based depreciation method would be more appropriate when requirements for application of non-depreciation approach are not satisfied. Since bridge and tunnel facilities show various patterns of deterioration and condition monitoring period by type and condition level, consumption-based depreciation method based on deterioration model would be appropriate. Therefore, it is necessary to have a reasonable asset management system to apply condition-based depreciation method and a periodic condition investigation to manage road assets well.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.117-124
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• 2020

In 2013, Diesl defined a nil clean ring as a ring of which all elements can be expressed as the sum of an idempotent and a nilpotent. Furthermore, in 2017, Y. Zhou, S. Sahinkaya, G. Tang studied nil clean group rings, finding both necessary condition and sufficient condition for a group ring to be a nil clean ring. We have proposed a necessary and sufficient condition for a group ring to be a uniquely nil clean ring. Additionally, we provided theorems for general nil clean group rings, and some examples of trivial-center groups of which group ring is not nil clean over any strongly nil clean rings.