• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.5
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• pp.734-740
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• 2010

We define and study the fuzzy nil radical of a fuzzy ideal of a commutative $\kappa$-semiring.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.3
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• pp.423-429
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• 2007

We define and study the fuzzy Jacobson radical of a ${\kappa}$-semiring. Also it is shown that the Jacobson radical of the quotient semiring R/FJR(R) of a ${\kappa}$-semiring by the fuzzy Jacobson radical FJR(R) is semisimple. And the algebraic properties of the fuzzy ideals FJR(R) and FJR(S) under a homomorphism from R onto S are also discussed.

• 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.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.147-154
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• 2000

In this paper, with the notion of fuzzy ${\kappa}$-ideals of semirings, we discuss and review several results described in [4].

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.249-261
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• 1997

We find a necessary and sufficient condition for a $\kappa$-confi-guration $\mathbb{X}$ in $\mathbb{P}^2$ to be in generic position. We obtain the number and degrees of minimal generators of some Gorenstein ideals of codimension 3 and so obtain their minimal free resolution s of these ideals.

• 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.

• Imaging Science in Dentistry
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• v.42 no.3
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• pp.129-137
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• 2012

Purpose: To compare different radiographic methods for assessing endodontically treated teeth. Materials and Methods: Root canal treatments were applied in 120 extracted mandibular teeth, which were divided into four groups: (1) ideal root canal treatment (60 teeth), (2) insufficient lateral condensation (20 teeth), (3) root canals filled short of the apex (20 teeth), (4) overfilled root canal treatment (20 teeth). The teeth were imaged using intraoral film, panoramic film, digital intraoral systems (CCD and PSP), CCD obtained with portable X-ray source, digital panoramic, and CBCT images obtained at 0.3 $mm^3$ and 0.2 $mm^3$ voxel size. Images were evaluated separately by three observers, twice. Kappa coefficients were calculated. The percentage of correct readings obtained from each modality was calculated and compared using a t-test (p<0.05). Results: The intra-observer kappa for each observer ranged between 0.327 and 0.849. The inter-observer kappa for each observer for both readings ranged between 0.312 and 0.749. For the ideal root canal treatment group, CBCT with 0.2 $mm^3$ voxel images revealed the best results. For insufficient lateral condensation, the best readings were found with periapical film followed by CCD and PSP. The assessment of teeth with root canals filled short of the apex showed the highest percentage of correct readings by CBCT and CCD. For the overfilled canal treatment group, PSP images and conventional periapical film radiographs had the best scores. Conclusion: CBCT was found to be successful in the assessment of teeth with ideal root canal treatment and teeth with canals filled short of the apex.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.65-69
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• 2001

For any closed subspace X of $\ell_p, \; 1<\kappa<\infty$, K(X) is proximinal in L(X), and if X is a Banach space with an unconditional shrinking basis, then K(X, c$_0$) is proximinal in L(X,$ \ell_\infty$).

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.425-435
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• 2003

In this paper, a new kind of matrices, i.e., $level-{\kappa}$ II-circulant matrices is considered. Algorithms for computing minimal polynomial of this kind of matrices are presented by means of the algorithm for the Grobner basis of the ideal in the polynomial ring. Two algorithms for finding the inverses of such matrices are also presented based on the Buchberger's algorithm.

• Journal of the Korean Society of Propulsion Engineers
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• v.20 no.3
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• pp.17-24
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• 2016

The reacting flows of gaseous hydrogen/liquid oxygen 2D coaxial shear injector with varying recess length are numerically analyzed. The standard ${\kappa}-e$ model and laminar flamelet model are adopted for the steady turbulent combustion with the ideal and real gas equations. As the recess length increases, the recirculating region in the combustion chamber expands and the vorticity is intensified. Also, the variations of temperature, products, and pressure are strongly related to the recess length. The results show that an efficient combustor can be obtained by the introduction of the recessed injector.