• Title/Summary/Keyword: linear quotients

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STRONG SHELLABILITY OF SIMPLICIAL COMPLEXES

  • Guo, Jin;Shen, Yi-Huang;Wu, Tongsuo
    • Journal of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1613-1639
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    • 2019
  • Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure strongly shellable complexes. Meanwhile, pure strongly shellable complexes can be characterized by the corresponding codimension one graphs. In addition, we show that the facet ideals of pure strongly shellable complexes have linear quotients.

The Convolution Sum $\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(1, 14),(2, 7),(1, 7)

  • Alaca, Ayse;Alaca, Saban;Ntienjem, Ebenezer
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.377-389
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    • 2019
  • We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.

A Study on the Effect of Neurofeedback Training on the Improvement of Brain Function & Baduk Strength for Child Baduk Players (바둑 학습 아동들의 뇌 기능과 기력 향상에 뉴로피드백 훈련이 미치는 영향에 관한 연구)

  • Bak, Ki-Ja;Yi, Seon-Gyu;Jeong, Soo-Hyun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.9 no.5
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    • pp.1399-1406
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    • 2008
  • This study has been made to research effect of neurofeedback training on the Brain Quotient and baduk strength whose EEC data were obtained both before and after the neurofeedback training from 15th June, to 15th September in 2007. Brain waves were measured on the frontal lobes of subjects (30 baduk players - the experimental group 15 under neuroffedback training and the control group 15 subjects) and analyzed by calculating eight brain quotients characterizing behaviors of EEG rhythms effectively. The results of the analysis show that the experimental group has the higher indexes Attention Quotient(left) p=.041, (right)p=.007, Stress Quotient (left) p=.020, and Stress Quotient (right) p=.019 show statistically significant difference between two groups. The research data show that the experimental group have the higher average than the control group in Baduk strength examination p=.021 after the neuroffedback training. As the brain waves are adjusted by timeseries linear analysis, the brain function quotients can reflect the functional states of the brain.

A Reserch on the Effect Neurofeedback Traing before & After About Emotional and Attention Deficit Characteristics by Timeseries Linear Analysis : for Primary Student (시계열 선형 분석을 통한 뉴로피드백 훈련 전, 후의 주의력 결핍 성향과 정서적 성향에 미치는 영향에 관한 연구)

  • Bak, Ki-Ja;Park, Pyung-Woon;Yi, Seon-Gyu
    • Journal of Information Technology Applications and Management
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    • v.14 no.4
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    • pp.43-59
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    • 2007
  • The purpose of the study was to examine the effectiveness of Neuro Feedback training by observing the pre and post brainwave measurement results of about 50 (experimental group 25. comparative group 25) subjects who have shown psychological difficulties in studying. attention deficit, and personalities. The study took place at Neuro Feedback training Center B. in between the months of July 2006 and May 2007. The methodology involved in the study included the Coloring Analysis Program of the Brain Quotient Test. As the brain waves are adjusted by timeseries linear analysis. the brain function quotients can reflect the functional states of the brain. Through the test, three parameters relaxation, attention and concentration-were initially measured for one minute each and the lowest parameter out of the three was selected as the training mode or improvement target. The training took place two or three times a week. for about 40 to 60 minutes per session. Because the clients have come to the training center at different times. the researcher sampled the results of only those who had attended more than 30 training sessions. The tool used to measure the psychological reaction was POMS (Profile of Mood State). while the tool used to measure the emotional and attention-deficit characteristics was the Amen Clinic ADD Type questionnaire. Hypothesis testing included t-test. The result of the study showed the Theta: SMR ratio of (left)p = .013. (right) p = .019. The result also confirmed the differences of both ATQ(left) p = .011. (right)p = .030 and SQ(left) p = .017. (right) p = .022. The result confirmed of emotional p = .000. attention-deficit characteristics p = .000. The result of the study suggest Neuro Feedback technique's possibility in positively affecting the subjects' mental state and attention-deficit characteristics.

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The review of safety against derailment on twisted track for Korean tilting train design (한국형 틸팅차량 설계의 비틀린 궤도상의 탈선안전도 검토)

  • Kim Nam-Po;Kim Jung-Seok;Park Tae-Won
    • Proceedings of the KSR Conference
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    • 2005.05a
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    • pp.299-307
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    • 2005
  • The 180 km/h Korean Tilting Train(TTX) which is now developing as a part of the Korean National R&D project, was elaborately designed. As the tilting trains run curve track with the $30\%$ higher speed than normal trains, the higher centrifugal and dynamic force are expected. Furthermore the complex tilting system increase the probability of failure. Therefore it is very important for tilting train to ensure safety against derailment under the various kind of failed condition in the middle of running as well as normal operating condition. The TTX train have the relatively high roll stiffness to improve the lateral ride comfort and to limit the roll displacement on the curve. But the higher roll stiffness increase the risk of derailment on the twisted track. This paper describes the study to review the safety against derailment caused by the wheel unloading on the severely twisted track. The worst combination of maximum cant change with maximum twist defect was established by numerical simulation. And also it was assumed that the air bag deflated and still the train run its speed limit. Those kind of assumption might be the worst case from the view point of wheel unloading derailment on the twisted track. The dynamic simulation was done by means of VAMPIRE S/W and non-linear transient analysis. We found that derailment quotients Q/P was only slightly influenced by track twist but the wheel unloading was greatly influenced. And we ascertained that the higher roll stiffness the higher wheel unloading. In case of air bag deflated situation, the wheel unloading reached up to $100\%$ which means the wheel lift or jumped. Therefore it was concluded that the design need to be improved to ensure the safety against derailment on the maximum twisted track in case of air bag deflated and tilting train's speed limit.

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A Study on the Effect of Neurofeedback Traing on the hearing impairments Student about Resistance Stress (청각장애 학생들의 일상적 스트레스 저항능력에 뉴로피드백 훈련이 미치는 영향 분석 연구)

  • Bak, Ki-Ja
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.11 no.9
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    • pp.3318-3324
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    • 2010
  • This study was to examine the effectiveness of neurofeedback training by observing the pre and post brainwave measurement results of about 16(Primary Student 6, middle school student10) student who have shown resistance stress and body stress, mental stress. The study was examined at S city M dong A hearing impairments student, from Mar. 2008 and to Feb. 2009. The methodology used in the study is the Coloring Analysis Program of the Brain Quotient Test. As the brain waves are adjusted by timeseries linear analysis, the brain function quotients can reflect the functional states of the brain. The training took place two times a week, for about 40 minutes per session. The result confirmed the differences of both resistance stress quotient and body stress, mental stress. The results of the analysis show that neurofeedback training plays positive role in changing the brain function. Therefore, the result of the study shows that there is possibility that Neuro Feedback technique might be positively affecting resistance stress of the hearing impairments student, relationship between neurofeedback training and stress among several categories.