• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.365-371
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• 2003

In this paper, we introduce metrics d, p and ${\mu}$ on a normed almost linear space (X, III.III). And we prove that above three metrics are equivalent if a normed almost linear space X has a basis and splits as X = W$_X$ + V$_X$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1335-1349
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• 2020

In this paper, we give an equivalent characterization for general (α, β)-metrics with reversible geodesics when the dimension of the manifold is greater than 2.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.641-648
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• 2000

It has been conjectured that, on a compact 3-dimensional manifold, a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics of volume 1 is Einstein. In this paper we find a sufficient condition that a critical point is Einstein. This condition is equivalent for a critical point ot be conformally flat. Its relationship with the Fisher-Marsden conjecture is also discussed.

• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2220-2226
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• 2018

Electric vehicles (EVs) are significant resources for demand response (DR). Thus, it is essential for EV aggregators to quantitatively evaluate their capability for DR. In this paper, a concept of dynamic equivalent battery (DEB) is proposed as a metric for evaluating the DR performance using EVs. The DEB is the available virtual battery for DR. The capacity of DEB is determined from stochastic calculation while satisfying the charging requirements of each EV, and it varies also with time. Further, a new indicator based on the DEB and time-varying electricity prices, named as value of DEB (VoDEB), is introduced to quantify the value of DEB coupled with the electricity prices. The effectiveness of the DEB and the VoDEB as metrics for the DR performance of EVs is verified with the simulations, where the difference of charging cost reduction between direct charging and optimized bidding methods is used to express the DR performance. The simulation results show that the proposed metrics accord well with the DR performance of an EV fleet. Thus, an EV aggregator may utilize the proposed concepts of DEB and VoDEB for designing an incentive scheme to EV users, who participate in a DR program.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.613-623
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• 2020

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.

• Structural Engineering and Mechanics
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• v.90 no.5
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• pp.505-515
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• 2024

In this study, obtaining theoretical stress-strain curves and determining the parameters defining the equivalent rectangular stress block were aimed for 3 and 4-layered rectangular Reinforced Concrete (RC) cross-sections subjected to flexure. For these aims, the analytical stress-strain model proposed by Hognestad was chosen for the concrete grades (20 MPa≤fck≤60 MPa) used in this study. The tensile strength of the concrete was neglected and the thickness of the concrete layers in the compression zone of the concrete cross-section was taken as equal. In addition, while concrete strength was kept constant within each layer, concrete strengths belonging to separate layers were increased from the neutral axis towards the outer face of the compression zone of the concrete cross-section. After the equivalent rectangular stress block parameters were determined by numerical iterations, variations of these parameters depending on concrete strength in layers and layer numbers were obtained. Finally, some analytical equations have been proposed to predict the equivalent stress block parameters for the 3 and 4-layered RC cross-sections and validities of these proposed equations were shown by different metrics in this study.

• The Journal of the Acoustical Society of Korea
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• v.25 no.3
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• pp.129-136
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• 2006

For the environmental noise assessments. A weighted equivalent noise level (LeqA) is used to measure the time varying environmental noise. However, it is not appropriately reflect various environmental noise features and human emotions. The human perception of the noise is affected largely by the psychoacoustic characteristics of noise as well as the sound pressure level In this study, the effective factors of noise qualify are analyzed using the subjective assessment and statistical analysis of environmental noise, such as road traffic noise. construction site noise, noise in daily living. and other. The analysis methodology is composed to three steps as follows : firstly, the values of the sound qualify metrics of various noise sources were analyzed. And to classify the noise sources, we conducted a cluster analysis using sound quality metrics. Secondly, subjective jury testing was carried out using the methods of paired comparisons and semantic differential. Finally, the correlation between the subjective parameters and the noise quality metrics were analyzed. As a result. the human perception characteristics of the various environmental noise are described in some physical parameters of the noise qualify metrics.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.85-90
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• 2000

On Riemannian manifolds of dimension 4 the Einstein condition is equivalent to the Thorpe condition. In this paper, we construct a few metrics which we Einstein but not Thorpe, and vice versa in dimensions larger than 4.

• Earthquakes and Structures
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• v.18 no.1
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• pp.27-44
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• 2020

This work presents a comparison of three performance-based seismic design methods (PBSD) as applied to plane steel frames having eccentric braces (EBFs) and buckling restrained braces (BRBFs). The first method uses equivalent modal damping ratios (ξ_k), referring to an equivalent multi-degree-of-freedom (MDOF) linear system, which retains the mass, the elastic stiffness and responds in the same way as the original non-linear MDOF system. The second method employs modal strength reduction factors (${\bar{q}}_k$) resulting from the corresponding modal damping ratios. Contrary to the behavior factors of code based design methods, both ξ_k and ${\bar{q}}_k$ account for the first few modes of significance and incorporate target deformation metrics like inter-storey drift ratio (IDR) and local ductility as well as structural characteristics like structural natural period, and soil types. Explicit empirical expressions of ξ_k and ${\bar{q}}_k$, recently presented by the present authors elsewhere, are also provided here for reasons of completeness and easy reference. The third method, developed here by the authors, is based on a hybrid force/displacement (HFD) seismic design scheme, since it combines the force-base design (FBD) method with the displacement-based design (DBD) method. According to this method, seismic design is accomplished by using a behavior factor (q_h), empirically expressed in terms of the global ductility of the frame, which takes into account both non-structural and structural deformation metrics. These expressions for q_h are obtained through extensive parametric studies involving non-linear dynamic analysis (NLDA) of 98 frames, subjected to 100 far-fault ground motions that correspond to four soil types of Eurocode 8. Furthermore, these factors can be used in conjunction with an elastic acceleration design spectrum for seismic design purposes. Finally, a comparison among the above three seismic design methods and the Eurocode 8 method is conducted with the aid of non-linear dynamic analyses via representative numerical examples, involving plane steel EBFs and BRBFs.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.707-711
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• 2004

Recently, the interests about noises have increased with the rapid development of our living environment Until now the estimation methods to sounds have used the equivalent levels. The sensitivities of human beings aren't considered in these methods. It's a situation to need new estimation methods for environmental noises. They must be analyzed by the characteristics of sounds before making the noise regulations newly. In this study, the noises were measured around our living environment And the frequency analysis, Sound Quality Metrics, the cluster analysis and so on are used to classify the environmental noises.