• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.17-26
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• 2014

In this paper, we present an algorithm for computing the number of points on the Jacobian varieties of genus 3 hyperelliptic curves of type $y^2=x^7+ax$ over finite prime fields. The problem of determining the group order of the Jacobian varieties of algebraic curves defined over finite fields is important not only arithmetic geometry but also curve-based cryptosystems in order to find a secure curve. Based on this, we provide the explicit formula of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety of hyperelliptic curve $y^2=x^7+ax$ over a finite field $\mathbb{F}_p$ with $p{\equiv}1$ modulo 12. Moreover, we also introduce some implementation results by using our algorithm.

• Journal of Wetlands Research
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• v.15 no.4
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• pp.609-618
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• 2013

Curve number (CN), originally developed, compiled by 'The Natural Resources Conservation Service (NRCS)', and has been widely used throughout the world. However, there is the uncertainty of CN derived from the use of antecedent moisture condition (AMC)/Antecedent Runoff Condition (ARC). As in Korea where nearly 70% covered by mountainous area, it is still not sufficient handbook precedent to guide or support the estimation of AMC/ARC. The failure to develop formal criteria of applying AMC/ ARC will be a gaping profession and results not only in uncertainty of CN estimation in particular, but also in designing appropriate structures in Korea as a whole. This paper is aiming at presenting a critical review of AMC/ARC and deriving a procedure to deal more realistically with event rainfall-runoff over wider variety of initial conditions. Proposed methods have been developed. It is based on modifying estimated runoff to observed runoff with coefficient of determination and then applying different algebraic expression with the verification of AMC by antecedent rainfall table of NEH-1964. The result shows that algebraic expression by Arnold et al. (1996) is the most appropriate for AMC/ARC and the results of AMC/ARC estimation criteria are generally very close to each other. Therefore, this algebraic expression might be applied in South Korea condition properly.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.26 no.3
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• pp.122-129
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• 2014

In order to extract shaft power from thermal energy in a R134a Rankine cycle as waste heat recovery system of a passenger car, a scroll expander has been designed. Algebraic spiral is adopted as the base curve for scroll wrap profile in the compact scroll design. About 19% reduction in scroll diameter is accomplished when compared to the conventional involute scroll. Performance analysis on the designed scroll expander shows that the expander efficiency is 85.5% at the vehicle speed of 120 km/hr and it decreases to 67.2% at 60 km/hr, provided that the scroll clearance is kept at 10 ${\mu}m$. The expander can produce shaft power equivalent to about 13~14% of the driving power within the speed range of 60~120 km/hr.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.24 no.2
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• pp.164-173
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• 2012

To study the applicability of a scroll type compressor to small capacity refrigerators, a R600a scroll compressor with algebraic scroll wrap has been designed. Its size and performance have been compared to a reciprocating type of the same displacement volume. By employing scroll wrap based on algebraic curve, high compression ratio can be accomplished without increasing the wrap angle much so that compact scroll may be obtained. Compared to a reciprocating one, the designed scroll compressor has diameter and height reduced by about 50% and 80%, respectively. By numerical simulation, it has been estimated that the scroll compressor provides 38.6% more cooling capacity than reciprocating type with 8.9% more power consumption, resulting in 27.3% increase in COP for ASHRAE low back pressure condition. With increasing the operating pressure ratio from 9.5 to 15.3, the overall compressor efficiency of the scroll compressor decreases from 72.6% to 65.2%, while that of the reciprocating compressor increases from 55.7% to 59.8%.

• Tribology and Lubricants
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• v.38 no.3
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• pp.84-92
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• 2022

In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, F_kij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that F_xxx(ŷ) = F_xyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as F_kij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λ_I=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of F_kij, i.e.(1 - λ_I) and p, Log|F_kij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.83-98
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• 2014

We reformulate an interpolation-based unique decoding algorithm of AG codes, using the theory of Gr$\ddot{o}$bner bases of modules on the coordinate ring of the base curve. The conceptual description of the reformulated algorithm lets us better understand the majority voting procedure, which is central in the interpolation-based unique decoding. Moreover the smaller Gr$\ddot{o}$bner bases imply smaller space and time complexity of the algorithm.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.225-237
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• 2015

In this article, we show that many of the genera that Giulietti and Fanali obtained from subfields of the GK curve can be obtained by using similar techniques used by Garcia, Stichtenoth and Xing. In the meantime, we obtain some new genera from the subfields of GK and generalized GK function fields.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.753-759
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• 1995

Let C be a smooth complex algebraic curve of genus g. For a divisor D on C, dim D means the dimension of the complete linear series $\mid$D$\mid$ containing D, which is the same as the projective dimension of the vector space of meromorphic functions f on C with divisor of poles $(f)_\infty \leq D$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.67-69
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• 2009

Recent work by Gwena and Teixidor i Bigas provides a characteristic-free proof of a part of a previous theorem by one of us, under a stronger numerical assumption. By using an intermediate result from the mentioned manuscript, here we present a simpler, characteristic-free proof of the whole original statement.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.377-386
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• 2011

For a smooth algebraic curve C of genus g $\geq$ 4, let $SU_C$(r, d) be the moduli space of semistable bundles of rank r $\geq$ 2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that $SU_C$(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree $\geq$ r with respect to the ampl generator of Pic($SU_C$(r, d)). In this paper, we study the locus swept out by the rational curves on $SU_C$(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on $SU_C$(r, d).