• 대한수학회지
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• 제45권6호
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• Korean Journal of Radiology
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• 제23권9호
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• pp.854-865
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• 2022

Photon-counting detector (PCD) CT is a new CT technology utilizing a direct conversion X-ray detector, where incident X-ray photon energies are directly recorded as electronical signals. The design of the photon-counting detector itself facilitates improvements in spatial resolution (via smaller detector pixel design) and iodine signal (via count weighting) while still permitting multi-energy imaging. PCD-CT can eliminate electronic noise and reduce artifacts due to the use of energy thresholds. Improved dose efficiency is important for low dose CT and pediatric imaging. The ultra-high spatial resolution of PCD-CT design permits lower dose scanning for all body regions and is particularly helpful in identifying important imaging findings in thoracic and musculoskeletal CT. Improved iodine signal may be helpful for low contrast tasks in abdominal imaging. Virtual monoenergetic images and material classification will assist with numerous diagnostic tasks in abdominal, musculoskeletal, and cardiovascular imaging. Dual-source PCD-CT permits multi-energy CT images of the heart and coronary arteries at high temporal resolution. In this special review article, we review the clinical benefits of this technology across a wide variety of radiological subspecialties.

• Korean Journal of Mathematics
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• 제29권4호
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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 Computer Science & Network Security
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• 제22권12호
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• pp.205-211
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• 2022

Performing the rituals of Hajj and Umrah is an obligation of Allah Almighty to all Muslims from all over the world. Millions of Muslims visit the holy mosques in Makkah every year to perform Hajj and Umrah. One of the most important pillars in Performing Hajj/Umrah is Tawaf and Sa'ay. Tawaf finished by seven rounds around the holy house (Al-Kabaa) and Sa'ay is also seven runs between As-Safa and Al-Marwa. Counting/knowing the number of runs during Tawaf/Sa'ay is one of the difficulties that many pilgrims face. The pilgrim's confusing for counting (Tawaf/Sa'ay) rounds finished at a specific time leads pilgrims to stay more time in Mataff bowl or Masa'a run causing stampedes and more crowded as well as losing the desired time for prayers to get closer to Almighty Allah in this holy place. These issues can be solved using effective crowd management systems for Tawaf/Sa'ay pillars, which is the topic of this research paper. While smart devices and their applications are gaining popularity in helping pilgrims for performing Hajj/Umrah activities efficiently, little has been dedicated for solving these issues. We present an autonomous Mobile-based framework for guiding pilgrims during Tawaf/Sa'ay pillars with the aid of GPS for points tracking and rounds counting. This framework is specially designed to prevent and manage stampedes during Tawaf/Sa'ay pillars, by helping pilgrims automatically counting the rounds during Tawaf/Sa'ay with supported Supplications (in written/audio form with different languages) from the Quran and Sunna'a.

• Journal of Electrical Engineering and Technology
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• 제6권3호
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• pp.391-396
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• 2011

The tracking pattern formed on the dielectric surface due to a surface electrical discharge exhibits fractal structure. In order to quantitatively investigate the fractal characteristics of the surface tracking pattern, the dielectric breakdown model has been employed to numerically generate the surface tracking pattern. In dielectric breakdown model, the pattern growth is determined stochastically by a probability function depending on the local electric potential difference. For the computation of the electric potential for all points of the lattice, a two-dimensional discrete Laplace equation is solved by mean of the successive over-relaxation method combined to the Gauss-Seidel method. The box counting method has been used to calculate the fractal dimensions of the simulated patterns with various exponent $\eta$ and breakdown voltage $\phi_b$. As a result of the simulation, it is found that the fractal nature of the surface tracking pattern depends strongly on $\eta$ and $\phi_b$.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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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 applied mathematics & informatics
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• 제22권1_2호
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• pp.339-350
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• 2006

The bifurcation point where a satellite component buds from another component is characterized by the existence of the common tangent line between the two osculating components appearing in the degree-n bifurcation set. We investigate the existence, location and number of bifurcation points for satellite components budding from the main component in the degree-n bifurcation set as well as a parametric boundary equation of the main component of the degree-n bifurcation set. Cusp points are also located on the boundary of the main component. Typical degree-n bifurcation sets and their components are illustrated with some computational results.

• 분석과학
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• 제27권3호
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• pp.153-160
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• 2014

세계적으로 석면분석방법에 관한 다양한 연구사례가 발표되고 있는 가운데, 분석방법의 차이에 따른 석면함유물질(ACM, Asbestos Containing Material) 결과에 대한 관심이 대두되고 있다. 본 연구에서는 균질성이 확보된 ACM 시료를 시야평가법(visual estimation method)과 포인트계수법(point counting method)의 분석결과에 대한 비교 평가를 통하여 분석기관 및 분석자의 신뢰성 향상과 더불어 편광현미경 분석의 기초자료를 확보고자 하였다. 석면분석은 정성분석과 정량분석으로 구분하였으며, 석면정량을 위한 방법은 EPA 600-R-93-116의 시야평가법과 포인트계수법으로 총 400지점을 계수하는 방법으로 실시하였다. 먼저 준비된 시료의 균질성을 분산분석을 이용하여 확인한 결과 이상이 없음을 확인하였다. 정성분석의 결과는 백석면과 갈석면으로 확인되었고 정량분석결과는 포인트계수법이 시야평가법과 비교하여 전체적인 석면함유량이 저평가되는 경향과 함께 포인트계수법은 분석과정이 조금 복잡하고 분석시간이 많이 소요되었다.

• Industrial Engineering and Management Systems
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• 제3권1호
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• pp.85-91
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• 2004

The writing styles of TIME and Newsweek are analyzed using a specially developed linguistic program. These two news magazines were chosen because of their wide popularity. As for the results, it became obvious that both the frequency curve of words and that of characters have not changed for the past 60 years. Also, we have found that the frequency curves have some inflection points and that the genre of English writings can be identified by these points. After counting the percentage of required vocabulary for junior high school students and high school students in English writings, we can derive the relative difficulties of them using fuzzy reasoning. Fuzzy rules are constructed using features of the characteristic curves. We feel it would be a good guide index when selecting textbooks or supplementary readers.

• Journal of the Korean Data Analysis Society
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• 제20권6호
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• pp.2711-2719
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• 2018

When an observable is described by a single value, the statistic significance may be estimated by construction of null distribution using permutation and counting the portion of it that exceeds the observed value by chance. Genome-wide association study usually focuses on the association measure between a single or interacting genotypes with a single phenotype. However investigation of common genotypes associated simultaneously on multiple phenotypes may involve the observables that should be described with multiple numbers. Statistical significance for such an observable would involve null distribution in multiple dimensions. In this study, extension of the p-value estimation process using null distribution in one dimension has been sought that may be applicable to two dimensional case. Comparison of the position of points within the set of points they form has been proposed to use a positioning parameter inspired by the extension of the Kolmogorov-Smirnov statistic to two dimensions.