• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1083-1096
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• 2012

For a given ideal I of a Noetherian ring R and an arbitrary integer ${\kappa}{\geq}-1$, we apply the concept of ${\kappa}$-regular sequences and the notion of ${\kappa}$-depth to give some results on modules called ${\kappa}$-Cohen Macaulay modules, which in local case, is exactly the ${\kappa}$-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any ${\kappa}$-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any ${\kappa}$-regular sequence is at most ${\kappa}$. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.487-497
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• 2006

The purpose of this paper is to describe the structure of the rings $\mathbb{Z}_{p^2}[X]/({\alpha}(X))$ with ${\alpha}(X)$ a monic polynomial and $\={X}^{\kappa}=0$ for some nonnegative integer ${\kappa}$. Especially we will see that any ideal of such rings can be generated by at most two elements of the special form and we will find the 'minimal' set of generators of the ideals. We indicate how to identify the isomorphism types of the ideals as $\mathbb{Z}_{p^2}-modules$ by finding the isomorphism types of the ideals of some particular ring. Also we will find the annihilators of the ideals by finding the most 'economical' way of annihilating the generators of the ideal.

• The Transactions of the Korea Information Processing Society
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• v.4 no.9
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• pp.2259-2268
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• 1997

Multistage interconnection networks(MINs) provide a high-bandwidth communication between processors and/or memory modules in a cost-effective way. In this paper, we propose a class of multipath MINs, called the Augmented Modified Delta(AMD) network, and analyze its performance and reliability. The salient features of the AMD network include fault-tolerant capability, modular structure, and high performance, which are essential for real-time parallel/distributed processing environments. The class of the AMD network retains well-known characteristics of the Kappa network, but it's design procedure is more systematic. Like Delta networks, all the AMD networks are topologically equivalent with each other.

• Journal of Environmental Science International
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• v.27 no.7
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• pp.531-541
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• 2018

Road freezing caused by snowfall during wintertime causes traffic congestion and many accidents. To prevent such problems, we developed, in this study, a system to predict road freezing based on weather forecast data and the freezing generation modules. The weather forecast data were obtained from a high-resolution model with 1 km resolution for Jeju Island from 00:00 KST on December 1, 2017, to 23:00 KST on February 28, 2018. The results of the weather forecast data show that index of agreement (IOA) temperature was higher than 0.85 at all points, and that for wind speed was higher than 0.7 except in Seogwipo city. In order to evaluate the results of the freezing predictions, we used model evaluation metrics obtained from a confusion matrix. These metrics revealed that, the Imacho module showed good performance in precision and accuracy and that the Karlsson module showed good performance in specificity and FP rate. In particular, Cohen's kappa value was shown to be excellent for both modules, demonstrating that the algorithm is reliable. The superiority of both the modules shows that the new system can prevent traffic problems related to road freezing in the Jeju area during wintertime.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.1
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• pp.25-31
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• 2004

The heat transfer characteristics of a plasma display panel has been investigated for cooling an electronic module. Hence, a two dimensional $\kappa-{\varepsilon}$ turbulent model was developed to predict the temperatures of the panel and module. The heat conduction was solve for the material region. To consider the mixed convection at the solid-fluid interfaces between the air and the panel and module, the energy equation was solved simultaneously. When the electronic module stands face to face with the panel, the temperatures of panel and module are lower than other arrangement due to the chimney effect. However the gap between the panel and module does not affect significantly the maximum temperature when the aspect ratio is less than 0.1. To maintain the maximum temperature of the module under a certain limit, the passage of air should be well designed by the optimal layout of electronic modules which have different heat emission.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.627-639
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• 2011

Hopf corings are dened in this work as coring objects in the category of algebras over a commutative ring R. Using the Dieudonn$\'{e}$ equivalences from [7] and [19], one can associate coring structures built from the Hopf algebra $F_p[x_0,x_1,{\ldots}]$, p a prime, with Hopf ring structures with same underlying connected Hopf algebra. We have that $F_p[x_0,x_1,{\ldots}]$ coring structures classify thus Hopf ring structures for a given Hopf algebra. These methods are applied to dene new ring products in the Hopf algebras underlying known Hopf rings that come from connective Morava ${\kappa}$-theory.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.879-897
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• 2013

Shannon entropy is one of the widely used randomness measures especially for cryptographic applications. However, the conventional entropy tests are less sensitive to the inter-bit dependency in random samples. In this paper, we propose new online randomness test schemes for true random number generators (TRNGs) based on the mutual information between consecutive ${\kappa}$-bit output blocks for testing of inter-bit dependency in random samples. By estimating the block entropies of distinct lengths at the same time, it is possible to measure the mutual information, which is closely related to the amount of the statistical dependency between two consecutive data blocks. In addition, we propose a new estimation method for entropies, which accumulates intermediate values of the number of frequencies. The proposed method can estimate entropy with less samples than Maurer-Coron type entropy test can. By numerical simulations, it is shown that the new proposed scheme can be used as a reliable online entropy estimator for TRNGs used by cryptographic modules.