• Journal for History of Mathematics
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• v.30 no.5
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• pp.289-304
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• 2017

The interdisciplinary study explores the discussion of actual infinity between Georg Cantor and Roman Catholic Church. Regarding the actual infinity, we first trace the theological background of Cantor by interpreting his correspondence and major works including ${\ddot{U}}ber$ die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche(1885) and Mitteilungen zur Lehre vom Transfiniten (1887), and then investigate his argumentation for two points at issue: (1) pantheism and (2) inconsistency of the necessity with freedom of God. In terms of mathematics and theology, Cantor defined the actual infinity(aphorismenon) as characterized by (1) the transfinite infinity(Transfinitum) and (2) the absolute infinity(Absolutum). Transfinitum is conceptualized here in mathematical terms as a multipliable actual infinity, whereas Absolutum is not as a multipliable actual infinity. The results imply that Cantor's own concept of Transfinitum and Absolutum is adequate for Roman Catholic theology as well as mathematics including the reflection principle.

• Proceedings of the Korea Information Processing Society Conference
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• 2010.11a
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• pp.779-782
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• 2010

Self-calibration에서 3차원 좌표의 복원은 호모그래피 행렬 H를 계산하면 얻을 수 있다. 이 호모그래피 행렬을 얻는 방법은 dual absolute quadric, Kruppa Equation(dual conic), plane at infinity(modulus constraint)를 사용하는 방법과 같이 세 가지 방법이 일반적으로 사용된다. 제안하는 방식은 dual absolute quadric을 사용한다. 카메라 내부 속성이 모든 뷰에서 동일하고 비틀림이나 영상의 원점이 중심이라는 가정을 두고 호모그래피 행렬 H를 계산한다. 실험을 통해서 주어진 가정으로 정밀한 복원이 가능함을 보였다.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.13-21
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• 2011

This mathematico-theological study addresses the Cantor's mathematics and theology of the infinite. From the scientific perspective, Cantor's landmark works opened the definition and logic of infinity in concreto, in abstracto, and in Deo. According to Cantor, the absolute infinite ${\Omega}$ could imply God's property beyond the actual infinite in physical and mathematical worlds.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.453-470
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• 2018

We study how to distinguish the parameters of the sparse autoregressive (AR) process from zero using a non-convex penalized estimation. A class of non-convex penalties are considered that include the smoothly clipped absolute deviation and minimax concave penalties as special examples. We prove that the penalized estimators achieve some standard theoretical properties such as weak and strong oracle properties which have been proved in sparse linear regression framework. The results hold when the maximal order of the AR process increases to infinity and the minimal size of true non-zero parameters decreases toward zero as the sample size increases. Further, we construct a practical method to select tuning parameters using generalized information criterion, of which the minimizer asymptotically recovers the best theoretical non-penalized estimator of the sparse AR process. Simulation studies are given to confirm the theoretical results.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.17-28
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• 2005

This paper aims to introduce a function and a role of history and philosophy of mathematics. Through historical examples it shows that history and philosophy of mathematics have the function to evaluate mathematics and the role to form it.

• Journal of Communications and Networks
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• v.16 no.2
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• pp.172-182
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• 2014

In this paper, we investigate the fundamental performance limits of the cooperative sensing using energy detection by considering the unlimited number of sensing nodes. Although a lot of cognitive radio research so far proposed various uses of energy detection because of its simplicity, the performance limits of energy detection have not been studied when a large number of sensing nodes exist. First, we show that when the sensing nodes see the independent and identically distributed channel conditions, then as the number of sensing nodes N goes to infinity, the OR rule of hard decision achieves zero of false alarm Pf for any given target probability of detection $\bar{P_d}$ irrespective of the non-zero received primary user signal to noise ratio ${\gamma}$. Second, we show that under the same condition, when the AND rule of hard decision is used, there exists a lower bound of $P_f$. Interestingly, however, for given $\bar{P_d}$, $P_f$ goes to 1 as N goes to infinity. Third, we show that when the soft decision is used, there exists a way of achieving 100% utilization of secondary user, i.e., the sensing time overhead ratio goes to zero so does $P_f$.We verify our analyses by performing extensive simulations of the proposed unlimited cooperative sensing. Finally, we suggest a way of incorporating the unlimited cooperative sensing into a practical cellular system such as long term evolutionadvanced by exploiting the existing frame structure of absolute blank subframe to implement the in-band sensing.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.45-59
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• 2018

The bi-material elastic system consisting of the pre-stressed hollow cylinder and pre-stresses surrounding infinite elastic medium is considered and it is assumed that the mentioned initial stresses in this system are caused with the compressing or stretching uniformly distributed normal forces acting at infinity in the direction which is parallel to the cylinder's axis. Moreover, it is assumed that on the internal surface of the cylinder the ring load which moves with constant velocity acts and within these frameworks it is required to determine the influence of the aforementioned initial stresses on the critical velocity of the moving load. The corresponding investigations are carried out within the framework of the so-called three-dimensional linearized theory of elastic waves in initially stresses bodies and the axisymmetric stress-strain state case is considered. The "moving coordinate system" method is used and the Fourier transform is employed for solution to the formulated mathematical problem and Fourier transformation of the sought values are determined analytically. However, the originals of those are determined numerically with the use of the Sommerfeld contour method. The critical velocity is determined from the criterion, according to which, the magnitudes of the absolute values of the stresses and displacements caused with the moving load approaches an infinity. Numerical results on the influence of the initial stresses on the critical velocity and interface normal and shear stresses are presented and discussed. In particular, it is established that the initial stretching (compressing) of the constituents of the system under consideration causes a decrease (an increase) in the values of the critical velocity.

• Sim-seong Yeon-gu
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• v.37 no.2
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• pp.149-183
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• 2022

The oracle of the I Ching, divination can be understood as 'synchronicity phenomenon' in analytic psychology. In order to experience divination actually, it requires a religious attitude that asks questions with a serious mind when a person is in trouble that consciousness reaches its limit. It is not just a passive attitude, but a modest, active attitude to ask what I can do now. The experience of the oracle of the I Ching connected to supra-consciousness is similar to 'active imagination'-talking with the archetype of collective unconsciousness-and is 'the process of finding the rhythm of Self-archetype, the absolute wisdom of unconsciousness.' One month before my father's death, I took care of him who couldn't communicate verbally and I divination with a question 'What can I do for my father and me now?' The I Ching's answer was hexagram 19 Lin 臨, nine at the beginning. It's message was '咸臨貞吉 joint approach. perseverance brings good fortune.' 志行正也 we must adhere perseveringly to what is right.' Through this phrase, I learned the attitude of waiting for life after death as if 'joyful obedient' to the providence of nature that spring comes after winter. And I found that keeping the touching emotion of meeting infinity (in analytical psychological terms, 'Self') with perseveration is to do the true meaning of life beyond popular money-mindedness. And six months before my father's death, I had a dream about the afterlife. In the process of interpreting that dream, I learned not only from the shock of the direct message that 'it is a truth that there is something after death,' but also the regeneration of the mind through introversion from the similarity between the closed ward and '黃泉'-chinese underworld through amplification. And I learned the importance of an open attitude to accept new things through the 'window to eternity' symbolized by the white iron gate. In my father's catholic funeral ritual, I had hope that the catholic doctrine 'Communio Sanctorum'-A spiral cycle in which the living and the dead help each other may be real as well as a symbol of the individuation process in which consciousness and unconsciousness interact in our minds. Through the consolation received through the funeral visit of many people I met in my life, I found the answer that the path to contact with infinity begins with loving the beings in front of me. I tried to understand this continuous experience by the perspective of analytical psychology.