• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.5
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• pp.528-535
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• 1988

This paper presents a constructing theory of variable arithmetic operation systems for computing multiplications and multiplicative inverse in GF(2**m) based on a modulo operation of degree on elements in Galois fields. The proposed multiplier is composed of a zero element control part, input element conversion part, inversion circuit, and output element conversion part. These systems can reduce reasonable circuit areas due to the common use of input/output element converison parts, and the PLA and module structure provice a variable property capable of convertible uses as arithmetic operation systems over different finite fields. This type of designs gives simple, regular, expandable, and concurrent properties suitable for VLSI implementation. Expecially, the multiplicative inverse circuit proposed here is expected to offer a characteristics of the high operation speed than conventional method.

• Bulletin of the Korean Chemical Society
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• v.27 no.7
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• pp.961-971
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• 2006

Shape controlled synthesis of inorganic nanocrystals is one of the important issues in materials chemistry due to their novel shape dependent properties. Although various shapes of nanocrystals have been developed, a systematic account on the shape control of these nanocrystals still remains an important subject in materials chemistry. In this article, we will overview the recent developments in the geometrical shape evolution of semiconductor and metal oxide nanocrystals obtained by nonhydrolytic synthetic methods. Many structurally unprecedented motifs have appeared as zero-dimesional (D) polyhedrons, one-D rods and wires, two-D plates and prisms, and other advanced shapes such as branched rods, stars, and inorganic dendrites. Important parameters which determine the geometrical shapes of nanocrystals are also illustrated. In addition, as a possible application of such nanocrystals for biomedical sciences, we further describe their utilizations for cancer diagnosis through nanocrystal-assisted magnetic resonance imaging (MRI).

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.2
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• pp.101-106
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• 1982

This study was undertaken to determine tensile properties and low-cycle fatigue behavior of 0.6%C high carbon steel used of structural purposes at temperatures up to 500.deg.C. In the low-cycle fatigue test the upper limit was decided by elongation(i.e. the total strain range), while the lower limit was defined by the load (i.e. zero load). The following results were obtained. Both, the ultimate tensile strength and low-cycle fatigue resistance attain the maximum values near 250.deg.C. Above this temperature the values decrease rapidly as the temperature increases. The low-cycle fatigue resistance decreases whenever there is an increase of the total strain range. Because the hardness of cycle fatigued specimen correlates cyclic hardening and cyclic softening, therefore the hardness of cycle fatigued specimen is smaller than that of the nonfatigued specimen at room temperature and 500.deg.C but much larger than the hardness of the nonfatigued specimen near 250.deg.C.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1887-1903
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• 2013

We continue the study of McCoy condition to analyze zero-dividing polynomials for the constant annihilators in the ideals generated by the coefficients. In the process we introduce the concept of ideal-${\pi}$-McCoy rings, extending known results related to McCoy condition. It is shown that the class of ideal-${\pi}$-McCoy rings contains both strongly McCoy rings whose non-regular polynomials are nilpotent and 2-primal rings. We also investigate relations between the ideal-${\pi}$-McCoy property and other standard ring theoretic properties. Moreover we extend the class of ideal-${\pi}$-McCoy rings by examining various sorts of ordinary ring extensions.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.31 no.4
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• pp.1-7
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• 1999

This study was carried out to simulate the change of various properties of recycled water when zero-discharge system was applied to a KOCC recycling process. contaminants such as chemical oxygen demand, anionic trash, and calcium hardness were gradually increased in the process water as the recycling was repeated . Especially, the increase of anionic trash and COD were closely related to the starch derived from corrugating adhesive in KOCC. Four kinds of water were compared in the preparation of handsheet to evaluate the performance of retention program. Waters used in this work were laboratory tab water, process water from Dong-II mill and the same one treated by UASB process, and closed white water prepared by KRICT. The result revealed that one the major factors fro reducing a retention power was the anioni trash accumulated in the recycled water.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2011.11a
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• pp.251-252
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• 2011

This study is to investigate experimentally the strength properties of mortar using recycled fine aggregates(RA) and blast furnace slag powder(BS) without cement according to type of fine aggregate. In the results of the study, compressive strength of RA was the highest. It can be considered that the results are due to the reaction of the non-hydration cement in RA to the latent hydraulicity reaction of the BS.

• Structural Engineering and Mechanics
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• v.33 no.5
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• pp.621-633
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• 2009

In this paper we compare the solution of the one-dimensional beam model and the numerical solution of the two-dimensional linearized elasticity problem for rectangular domain of the beam-like form. We first derive the beam model starting from the two-dimensional linearized elasticity, the same way it is derived from the three-dimensional linearized elasticity. Then we present the numerical solution of the two-dimensional problem by finite element method. As expected the difference of two approximations becomes smaller as the thickness of the beam tends to zero. We then analyze the applicability of the one-dimensional model and verify the main properties of the beam modeling for thin beams.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.721-734
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• 2014

Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph $T({\Gamma}(M))$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $m+n{\in}T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_0({\Gamma}(M))$ and $T_0({\Gamma}(M))$ of $T({\Gamma}(M))$, with vertices $T(M){\backslash}\{0\}$ and $M{\backslash}\{0\}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.

• Proceedings of the KIEE Conference
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• 1994.07b
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• pp.1295-1297
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• 1994

At 34 at% Co-Fe, the aluminum anodic oxidized (alumite) films of particle diameter $150{\AA}$ have large perpendicular anisotropy energy and high coercive force. However, for the samples of particle diameter larger than $450{\AA}$, the bottom of each particle forms abnormal part called branch-shaped different from that of particle diameter $150{\AA}$. In this case the magnetic anisotropy energy Ku was about zero at the compositions of 45 and 75 at% Co. Furthermore, at tile compositions from 50 to 70 at% Co, the values of Ku became negative value. We confirmed that Fe-C deposited the bottom of particle orients very strongly and it has a large influence upon the magnetic anisotropy energy.