• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.115-141
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• 2023

We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup {exp tX} is a normal nilpotent subgroup commuting with {exp tX}, and X is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-Kähler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension 5 and those of dimension 7 whose Kähler reduction in the above sense is abelian.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2680-2700
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• 2017

Finite field arithmetic over GF($2^m$) is used in a variety of applications such as cryptography, coding theory, computer algebra. It is mainly used in various cryptographic algorithms such as the Elliptic Curve Cryptography (ECC), Advanced Encryption Standard (AES), Twofish etc. The multiplication in a finite field is considered as highly complex and resource consuming operation in such applications. Many algorithms and architectures are proposed in the literature to obtain efficient multiplication operation in both hardware and software. In this paper, a modified serial multiplication algorithm with interleaved modular reduction is proposed, which allows for an efficient realization of a sequential polynomial basis multiplier. The proposed sequential multiplier supports multiplication of any two arbitrary finite field elements over GF($2^m$) for generic irreducible polynomials, therefore made versatile. Estimation of area and time complexities of the proposed sequential multiplier is performed and comparison with existing sequential multipliers is presented. The proposed sequential multiplier achieves 50% reduction in area-delay product over the best of existing sequential multipliers for m = 163, indicating an efficient design in terms of both area and delay. The Application Specific Integrated Circuit (ASIC) and the Field Programmable Gate Array (FPGA) implementation results indicate a significantly less power-delay and area-delay products of the proposed sequential multiplier over existing multipliers.

• Wind and Structures
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• v.21 no.5
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• pp.461-487
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• 2015

In recent years, the Graphics Processing Unit (GPU) has become a competitive computing technology in comparison with the standard Central Processing Unit (CPU) technology due to reduced unit cost, energy and computing time. This paper describes the derivation and implementation of GPU-based algorithms for the analysis of wind loading uncertainty on high-rise systems, in line with the research field of probability-based wind engineering. The study begins by presenting an application of the GPU technology to basic linear algebra problems to demonstrate advantages and limitations. Subsequently, Monte-Carlo integration and synthetic generation of wind turbulence are examined. Finally, the GPU architecture is used for the dynamic analysis of three high-rise structural systems under uncertain wind loads. In the first example the fragility analysis of a single degree-of-freedom structure is illustrated. Since fragility analysis employs sampling-based Monte Carlo simulation, it is feasible to distribute the evaluation of different random parameters among different GPU threads and to compute the results in parallel. In the second case the fragility analysis is carried out on a continuum structure, i.e., a tall building, in which double integration is required to evaluate the generalized turbulent wind load and the dynamic response in the frequency domain. The third example examines the computation of the generalized coupled wind load and response on a tall building in both along-wind and cross-wind directions. It is concluded that the GPU can perform computational tasks on average 10 times faster than the CPU.

• The KIPS Transactions:PartD
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• v.11D no.1
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• pp.39-50
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• 2004

GML proposed to offer interoperability of geography information is specifying various dynamic object schema for application in the wireless environment. These GML dynamic object schema supports the expression of moving objects that the position and shape change consecutively over time, so practical use of GML is increased in location-based service that provides various application services based on location information of moving objects. In particular, the conventional query languages about GML have been studied with priority given to the integration of geographic information, the support of spatial operations, and etc. However, it lacks the support for moving objects queries. Therefore, in this paper, we propose the moving objects query language that supports moving objects queries for GML documents by extension of XQuery that is standard in query language. Also, data model, algebra operation and various moving objects operators for the proposed query language are designed, and we apply the proposed query language to tornado government organization system to show that the proposed query language can be used effectively in various location-based service.

• Korean Journal of Optics and Photonics
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• v.20 no.2
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• pp.110-117
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• 2009

This work introduces the uncertainty evaluation formulation on color measurement of light sources and display devices, such as CIE 1931 (x, y) chromaticity, CIE 1960 (u, v) chromaticity, correlated color temperature, and distribution temperature. All the mentioned quantities are reduced from spectral data in the visible range, for which uncertainties are strongly correlated between different wavelengths. Using matrix algebra we have formulated the uncertainty propagation from the SI- traceable spectral irradiance standard to the individual color related measurement quantities taking the correlation between wavelengths into account. As a result, we have demonstrated uncertainty evaluation examples of 3 types of light sources: CIE illuminant A, LED white light, and LCD white light. This method can be applied to any other quantities based on spectral measurement such as solar irradiance, material color measurement, etc.