• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.53 no.1
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• pp.8-15
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• 2004

In order to scheme the optimal assumption that satisfies the travel demand, it should be review the elements that affect on determining the headway, which are signal systems, line shape, vehicle(Light Rail Transit) performance, and so on. When applying the conventional signal systems, including Fixed Block System and Moving Block System, It was confirmed whether or not satisfy the requirements of target line with the way of a numerical formula reviewing and Train performance Simulation on the main line, station, depot, and so forth. Therefore, it should be used as references that decide target line and each sub-system after identifying the compliances for Minimum Headway to Moving Block System.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.985-998
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• 1997

For n random strips chosen so as to meet a fixed bounded convex set K of the plane we let $\nu$ be the number of intersection regions that meet K. We develop the integral formula for the mean value of $\nu$ and $\nu^2$ involving the area and the perimeter of K and the breadths of the strips. We get some geometric inequalities in way of studying integral geometry.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.655-665
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• 2014

The number of topologies (non-homeomorphic topologies) on a fixed finite set having n elements are now known up to n = 18 (n = 16 respectively) but still no complete formula yet. There are one to one correspondences among topologies, preorders and transitive digraphs on a given finite set. In this article, we enumerate topologies and non-homeomorphic topologies whose underlying graph is a given finite simple graph.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.745-757
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• 2004

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Let f : G $\longrightarrow$ G be an endomorphism between the fundamental group of the mapping torus. Extending Jiang and Ferrario's works on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets of f relative to Reidemeister sets on suspension groups. In particular, if f is an automorphism, an similar formula for Reidemeister orbit sets of f relative to Reidemeister sets on given groups is also proved.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• International Journal of Naval Architecture and Ocean Engineering
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• v.5 no.2
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• pp.313-323
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• 2013

Offshore floating structures have so-called moonpool in the centre area for the purpose of drilling, installation of subsea structures, recovery of Remotely-Operated Vehicle (ROV) and divers. However, this vertical opening has an effect on the operating performance of floating offshore structure in the vicinity of moonpool resonance frequency; piston mode and sloshing mode. Experimental study based on model test was carried out. Moonpool resonance of floating offshore structure on fixed condition and motion free condition were investigated. And, the effect of cofferdam which is representative inner structure inside moonpool was examined. Model test results showed that Molin's theoretical formula can predict moonpool resonance on fixed condition quite accurately. However, motion free condition has higher resonance frequency when it is compared with that of motion fixed. The installation of cofferdam moves resonance frequency to higher region and also generates secondary resonance at lower frequency. Furthermore, it was found that cofferdam was the cause of generating waves in the longitudinal direction when the vessel was in beam sea.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.45 no.9
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• pp.8-13
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• 2008

Noise in homogeneous extrinsic semiconductor samples is calculated due to distributed diffusion noise sources. As the length of the device shrinks at a fixed bias voltage, the ac-wise short-circuit noise current shows excess noise as well as thermal noise spectra. This excess noise behaves like a full shot noise when the channel length becomes very small compared with the extrinsic Debye length. For the first time, the analytic formula of the excess noise in extrinsic semiconductors from velocity-fluctuation noise sources is given for finite frequencies. This formula shows the interplay between transit time, dielectric relaxation time, and velocity relaxation time in determining the terminal noise current as well as the carrier density fluctuation. As frequency increases, the power spectral density of the excess noise rolls off. This formula sheds light on noise in nanoscale MOSFETs where quasi-ballistic transport plays an important role in carrier transport and noise.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1A
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• pp.79-87
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• 2008

This paper investigates the in-plane stability of fixed shallow arches. The shape of the arches is parabolic and the uniformly distributed load is used in the study. The nonlinear governing equilibrium equation of the general arch is adopted to derive the incremental form of the load-displacement relationship and the buckling load of the fixed shallow arches. From the results, it is found that buckling modes (symmetric or asymmetric) of the arches are closely related to the dimensionless rise H, which is the function of slenderness ratio and the rise to span ratio of such arches. Moreover, the threshold of different buckling modes and buckling load for fixed shallow arches are proposed. A series of finite element analysis are conducted and then compared with proposed ones. From the comparative study, the proposed formula provides the good prediction of the buckling load of fixed shallow arches.

• Journal of the Korean Home Economics Association
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• v.39 no.10
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• pp.97-109
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• 2001

It is thought that a composition of trousers is related to fabrics with single breadth. Therefore, trousers are designed with pattern using this fabrics with single breadth. However, in the old pattern of trousers, the breadth of 33cm-35cm was not considered in designing patterns. In this context, deciding which pattern design is better is not easy as there are a variety of estimation methods. So in this study, standardization of drafting is pursued by an objective pattern design. For this, a base angle of the trouser closely relating to a form and function was measured and using the height and the base angle, a trouser pattern design was tried. For a measurement of the base angle, 5 subject were selected. They are 25-29 year-old male graduates with fine physical standard. The base angle was measured with symphysis pubis point as a standard when subjects sat with their legs crossed, when they stood with their legs open (not forced artificially) and when they laid down with their legs open. The distance between a knee inside joint and knees was measured three times and the resultant value was used for the pattern design. For a design of trousers, the height was applied and the base angle was fixed. As a pattern drawing, using the height, a base angle and circumference of the hip, a trouser was designed. The production method for the pattern design is as follow: (1) The length formula, is height + $\frac{height}{2}$ (2) The hip girth formula is $\frac{hipgirth}{2}$ - $\frac{hipgirth}{20}$(3) A crotch angle is fixed at $72^{\circ}$. (4) The ratio of outer leg length to leg width is 5 : 8. (5) The component ratio of the upper outer leg length to the pant length is 5 : 8. (6) The ratio of the division point of front right inner leg length and left inner width to upper outer leg length is 5 : 8.